Mathematical and Computational Applications

Research

21 pages, 1445 KiB

Open AccessArticle

Model-Based Assessment of Elastic Material Parameters in Rheumatic Heart Disease Patients and Healthy Subjects

by Mary A. Familusi, Sebastian Skatulla, Jagir R. Hussan, Olukayode O. Aremu, Daniel Mutithu, Evelyn N. Lumngwena, Freedom N. Gumedze and Ntobeko A. B. Ntusi

Math. Comput. Appl. 2023, 28(6), 106; https://doi.org/10.3390/mca28060106 - 1 Nov 2023

Cited by 1 | Viewed by 2350

Abstract

Non-invasive measurements are important for the development of new treatments for heart failure, which is one of the leading causes of death worldwide. This study aimed to develop realistic subject-specific computational models of human biventricles using clinical data. Three-dimensional finite element models of [...] Read more.

Non-invasive measurements are important for the development of new treatments for heart failure, which is one of the leading causes of death worldwide. This study aimed to develop realistic subject-specific computational models of human biventricles using clinical data. Three-dimensional finite element models of the human ventricles were created using cardiovascular magnetic resonance images of rheumatic heart disease (RHD) patients and healthy subjects. The material parameter optimization uses inverse modeling based on the finite element method combined with the Levenberg–Marquardt method (LVM) by targeting subject-specific hemodynamics. The study of elastic myocardial parameters between healthy subjects and RHD patients showed an elevated stiffness in diseased hearts. In particular, the anisotropic material behavior of the healthy and diseased cardiac tissue significantly differed from one another. Furthermore, as the LVEF decreased, the stiffness and its orientation-dependent parameters increased. The simulation-derived LV myocardial circumferential and longitudinal stresses were negatively associated with the LVEF. The sensitivity analysis result demonstrated that the observed significant difference between the elastic material parameters of diseased and healthy myocardium was not exclusively attributable to an increased LVEDP in the diseased heart. These results could be applied to future computational studies for developing heart failure treatment. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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16 pages, 5085 KiB

Open AccessArticle

A New Method for Improving Inverse Finite Element Method Material Characterization for the Mooney–Rivlin Material Model through Constrained Optimization

by John Dean Van Tonder, Martin Philip Venter and Gerhard Venter

Math. Comput. Appl. 2023, 28(4), 78; https://doi.org/10.3390/mca28040078 - 24 Jun 2023

Cited by 1 | Viewed by 3187

Abstract

The inverse finite element method is a technique that can be used for material model parameter characterization. The literature shows that this approach may get caught in the local minima of the design space. These local minimum solutions often fit the material test [...] Read more.

The inverse finite element method is a technique that can be used for material model parameter characterization. The literature shows that this approach may get caught in the local minima of the design space. These local minimum solutions often fit the material test data with small errors and are often mistaken for the optimal solution. The problem with these sub-optimal solutions becomes apparent when applied to different loading conditions where significant errors can be witnessed. The research of this paper presents a new method that resolves this issue for Mooney–Rivlin and builds on a previous paper that used flat planes, referred to as hyperplanes, to map the error functions, isolating the unique optimal solution. The new method alternatively uses a constrained optimization approach, utilizing equality constraints to evaluate the error functions. As a result, the design space’s curvature is taken into account, which significantly reduces the amount of variation between predicted parameters from a maximum of

1.934

% in the previous paper down to

0.1882

% in the results presented here. The results of this study demonstrate that the new method not only isolates the unique optimal solution but also drastically reduces the variation in the predicted parameters. The paper concludes that the presented new characterization method significantly contributes to the existing literature. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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20 pages, 6490 KiB

Open AccessArticle

Inducing Perceptual Dominance with Binocular Rivalry in a Virtual Reality Head-Mounted Display

by Julianne Blignaut, Martin Venter, David van den Heever, Mark Solms and Ivan Crockart

Math. Comput. Appl. 2023, 28(3), 77; https://doi.org/10.3390/mca28030077 - 17 Jun 2023

Viewed by 2287

Abstract

Binocular rivalry is the perceptual dominance of one visual stimulus over another. Conventionally, binocular rivalry is induced using a mirror-stereoscope—a setup involving mirrors oriented at an angle to a display. The respective mirror planes fuse competing visual stimuli in the observer’s visual field [...] Read more.

Binocular rivalry is the perceptual dominance of one visual stimulus over another. Conventionally, binocular rivalry is induced using a mirror-stereoscope—a setup involving mirrors oriented at an angle to a display. The respective mirror planes fuse competing visual stimuli in the observer’s visual field by projecting the stimuli through the stereoscope to the observed visual field. Since virtual-reality head-mounted displays fuse dichoptic vision in a similar way, and since virtual-reality head-mounted displays are more versatile and more readily available than mirror stereoscopes, this study investigated the efficacy of using a virtual-reality headset (Oculus Rift-S) as an alternative to using a mirror stereoscope to study binocular rivalry. To evaluate the validity of using virtual-reality headsets to induce visual dominance/suppression, two identical experimental sequences—one using a conventional mirror stereoscope and one using a virtual-reality headset—were compared and evaluated. The study used Gabor patches at different orientations to induce binocular rivalry and to evaluate the efficacy of the two experiments. Participants were asked to record all instances of perceptual dominance (complete suppression) and non-dominance (incomplete suppression). Independent sample t-tests confirmed that binocular rivalry with stable vergence was successfully induced for the mirror-stereoscope experiment (t = −4.86; p ≤ 0.0001) and the virtual-reality experiment (t = −9.41; p ≤ 0.0001). Using ANOVA to compare Gabor patch pairs of gratings at +45°/−45° orientations presented in both visual fields, gratings at 0°/90° orientations presented in both visual fields, and mixed gratings (i.e., unconventional grating pairs) presented in both visual fields, the performance of the two experiments was evaluated by comparing observation duration in seconds (F = 0.12; p = 0.91) and the alternation rate per trial (F = 8.1; p = 0.0005). The differences between the stimulus groups were not statistically significant for the observation duration but were significantly different based on the alternation rates per trial. Moreover, ANOVA also showed that the dominance durations (F = 114.1; p < 0.0001) and the alternation rates (F = 91.6; p < 0.0001) per trial were significantly different between the mirror-stereoscope and the virtual-reality experiments, with the virtual-reality experiment showing an increase in alternation rate and a decrease in observation duration. The study was able to show that a virtual-reality head-mounted display can be used as an effective and novel alternative to induce binocular rivalry, but there were some differences in visual bi-stability between the two methods. This paper discusses the experimental measures taken to minimise piecemeal rivalry and to evaluate perceptual dominance between the two experimental designs. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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15 pages, 508 KiB

Open AccessArticle

Numerical Aspects of a Continuum Sintering Model Formulated in the Standard Dissipative Framework

by Sebastian Stark

Math. Comput. Appl. 2023, 28(3), 69; https://doi.org/10.3390/mca28030069 - 17 May 2023

Cited by 2 | Viewed by 1395

Abstract

Robust and computationally efficient numeric algorithms are required to simulate the sintering process of complex ceramic components by means of the finite element method. This work focuses on a thermodynamically consistent sintering model capturing the effects of both, viscosity and elasticity, within the [...] Read more.

Robust and computationally efficient numeric algorithms are required to simulate the sintering process of complex ceramic components by means of the finite element method. This work focuses on a thermodynamically consistent sintering model capturing the effects of both, viscosity and elasticity, within the standard dissipative framework. In particular, the temporal integration of the model by means of several implicit first and second order accurate one step time integration methods is discussed. It is shown in terms of numerical experiments on the material point level that the first order schemes exhibit poor performance when compared to second order schemes. Further numerical experiments indicate that the results translate directly to finite element simulations. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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18 pages, 9233 KiB

Open AccessArticle

Intermediate Encoding Layers for the Generative Design of 2D Soft Robot Actuators: A Comparison of CPPN’s, L-Systems and Random Generation

by Martin Philip Venter and Naudé Thomas Conradie

Math. Comput. Appl. 2023, 28(3), 68; https://doi.org/10.3390/mca28030068 - 15 May 2023

Viewed by 1848

Abstract

This paper introduced a comparison method for three explicitly defined intermediate encoding methods in generative design for two-dimensional soft robotic units. This study evaluates a conventional genetic algorithm with full access to removing elements from the design domain using an implicit random encoding [...] Read more.

This paper introduced a comparison method for three explicitly defined intermediate encoding methods in generative design for two-dimensional soft robotic units. This study evaluates a conventional genetic algorithm with full access to removing elements from the design domain using an implicit random encoding layer, a Lindenmayer system encoding mimicking biological growth patterns and a compositional pattern producing network encoding for 2D pattern generation. The objective of the optimisation problem is to match the deformation of a single actuator unit with a desired target shape, specifically uni-axial elongation, under internal pressure. The study results suggest that the Lindenmayer system encoding generates candidate units with fewer function evaluations than the traditional implicitly encoded genetic algorithm. However, the distribution of constraint and internal energy is similar to that of the random encoding, and the Lindenmayer system encoding produces a less diverse population of candidate units. In contrast, despite requiring more function evaluations than the Lindenmayer System encoding, the Compositional Pattern Producing Network encoding produces a similar diversity of candidate units. Overall, the Compositional Pattern Producing Network encoding results in a proportionally higher number of high-performing units than the random or Lindenmayer system encoding, making it a viable alternative to a conventional monolithic approach. The results suggest that the compositional pattern producing network encoding may be a promising approach for designing soft robotic actuators with desirable performance characteristics. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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15 pages, 6201 KiB

Open AccessArticle

The Use of Computational Fluid Dynamics for Assessing Flow-Induced Acoustics to Diagnose Lung Conditions

by Khanyisani Mhlangano Makhanya, Simon Connell, Muaaz Bhamjee and Neil Martinson

Math. Comput. Appl. 2023, 28(3), 64; https://doi.org/10.3390/mca28030064 - 3 May 2023

Viewed by 2171

Abstract

Pulmonary diseases are a leading cause of illness and disability globally. While having access to hospitals or specialist clinics for investigations is currently the usual way to characterize the patient’s condition, access to medical services is restricted in less resourced settings. We posit [...] Read more.

Pulmonary diseases are a leading cause of illness and disability globally. While having access to hospitals or specialist clinics for investigations is currently the usual way to characterize the patient’s condition, access to medical services is restricted in less resourced settings. We posit that pulmonary disease may impact on vocalization which could aid in characterizing a pulmonary condition. We therefore propose a new method to diagnose pulmonary disease analyzing the vocal and cough changes of a patient. Computational fluid dynamics holds immense potential for assessing the flow-induced acoustics in the lungs. The aim of this study is to investigate the potential of flow-induced vocal-, cough-, and lung-generated acoustics to diagnose lung conditions using computational fluid dynamics methods. In this study, pneumonia is the model disease which is studied. The hypothesis is that using a computational fluid dynamics model for assessing the flow-induced acoustics will accurately represent the flow-induced acoustics for healthy and infected lungs and that possible modeled difference in fluid and acoustic behavior between these pathologies will be tested and described. Computational fluid dynamics and a lung geometry will be used to simulate the flow distribution and obtain the acoustics for the different scenarios. The results suggest that it is possible to determine the difference in vocalization between healthy lungs and those with pneumonia, using computational fluid dynamics, as the flow patterns and acoustics differ. Our results suggest there is potential for computational fluid dynamics to enhance understanding of flow-induced acoustics that could be characteristic of different lung pathologies. Such simulations could be repeated using machine learning with the final objective to use telemedicine to triage or diagnose patients with respiratory illness remotely. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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23 pages, 49612 KiB

Open AccessArticle

Evaluation of Physics-Informed Neural Network Solution Accuracy and Efficiency for Modeling Aortic Transvalvular Blood Flow

by Jacques Francois Du Toit and Ryno Laubscher

Math. Comput. Appl. 2023, 28(2), 62; https://doi.org/10.3390/mca28020062 - 14 Apr 2023

Cited by 1 | Viewed by 4558

Abstract

Physics-Informed Neural Networks (PINNs) are a new class of machine learning algorithms that are capable of accurately solving complex partial differential equations (PDEs) without training data. By introducing a new methodology for fluid simulation, PINNs provide the opportunity to address challenges that were [...] Read more.

Physics-Informed Neural Networks (PINNs) are a new class of machine learning algorithms that are capable of accurately solving complex partial differential equations (PDEs) without training data. By introducing a new methodology for fluid simulation, PINNs provide the opportunity to address challenges that were previously intractable, such as PDE problems that are ill-posed. PINNs can also solve parameterized problems in a parallel manner, which results in favorable scaling of the associated computational cost. The full potential of the application of PINNs to solving fluid dynamics problems is still unknown, as the method is still in early development: many issues remain to be addressed, such as the numerical stiffness of the training dynamics, the shortage of methods for simulating turbulent flows and the uncertainty surrounding what model hyperparameters perform best. In this paper, we investigated the accuracy and efficiency of PINNs for modeling aortic transvalvular blood flow in the laminar and turbulent regimes, using various techniques from the literature to improve the simulation accuracy of PINNs. Almost no work has been published, to date, on solving turbulent flows using PINNs without training data, as this regime has proved difficult. This paper aims to address this gap in the literature, by providing an illustrative example of such an application. The simulation results are discussed, and compared to results from the Finite Volume Method (FVM). It is shown that PINNs can closely match the FVM solution for laminar flow, with normalized maximum velocity and normalized maximum pressure errors as low as

5.74 %

and

9.29 %

, respectively. The simulation of turbulent flow is shown to be a greater challenge, with normalized maximum velocity and normalized maximum pressure errors only as low as

41.8 %

and

113 %

, respectively. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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14 pages, 7716 KiB

Open AccessArticle

A Computational Magnetohydrodynamic Modelling Study on Plasma Arc Behaviour in Gasification Applications

by Quinn G. Reynolds, Thokozile P. Kekana and Buhle S. Xakalashe

Math. Comput. Appl. 2023, 28(2), 60; https://doi.org/10.3390/mca28020060 - 12 Apr 2023

Viewed by 2275

Abstract

The application of direct-current plasma arc furnace technology to the problem of coal gasification is investigated using computational multiphysics models of the plasma arc inside such units. An integrated modelling workflow for the study of DC plasma arc discharges in synthesis gas atmospheres [...] Read more.

The application of direct-current plasma arc furnace technology to the problem of coal gasification is investigated using computational multiphysics models of the plasma arc inside such units. An integrated modelling workflow for the study of DC plasma arc discharges in synthesis gas atmospheres is presented. The thermodynamic and transport properties of the plasma are estimated using statistical mechanics calculations and are shown to have highly non-linear dependencies on the gas composition and temperature. A computational magnetohydrodynamic solver for electromagnetically coupled flows is developed and implemented in the OpenFOAM^® framework, and the behaviour of three-dimensional transient simulations of arc formation and dynamics is studied in response to different plasma gas compositions and furnace operating conditions. To demonstrate the utility of the methods presented, practical engineering results are obtained from an ensemble of simulation results for a pilot-scale furnace design. These include the stability of the arc under different operating conditions and the dependence of voltage–current relationships on the arc length, which are relevant in understanding the industrial operability of plasma arc furnaces used for waste coal gasification. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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13 pages, 1202 KiB

Open AccessEditor’s ChoiceArticle

A Parallel Solver for FSI Problems with Fictitious Domain Approach

by Daniele Boffi, Fabio Credali, Lucia Gastaldi and Simone Scacchi

Math. Comput. Appl. 2023, 28(2), 59; https://doi.org/10.3390/mca28020059 - 10 Apr 2023

Cited by 2 | Viewed by 2163

Abstract

We present and analyze a parallel solver for the solution of fluid structure interaction problems described by a fictitious domain approach. In particular, the fluid is modeled by the non-stationary incompressible Navier–Stokes equations, while the solid evolution is represented by the elasticity equations. [...] Read more.

We present and analyze a parallel solver for the solution of fluid structure interaction problems described by a fictitious domain approach. In particular, the fluid is modeled by the non-stationary incompressible Navier–Stokes equations, while the solid evolution is represented by the elasticity equations. The parallel implementation is based on the PETSc library and the solver has been tested in terms of robustness with respect to mesh refinement and weak scalability by running simulations on a Linux cluster. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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14 pages, 2817 KiB

Open AccessArticle

Digital Twin Hybrid Modeling for Enhancing Guided Wave Ultrasound Inspection Signals in Welded Rails

by Dineo A. Ramatlo, Daniel N. Wilke and Philip W. Loveday

Math. Comput. Appl. 2023, 28(2), 58; https://doi.org/10.3390/mca28020058 - 10 Apr 2023

Cited by 4 | Viewed by 2514

Abstract

Guided wave ultrasound (GWU) systems have been widely used for monitoring structures such as rails, pipelines, and plates. In railway tracks, the monitoring process involves the complicated propagation of waves over several hundred meters. The propagating waves are multi-modal and interact with discontinuities [...] Read more.

Guided wave ultrasound (GWU) systems have been widely used for monitoring structures such as rails, pipelines, and plates. In railway tracks, the monitoring process involves the complicated propagation of waves over several hundred meters. The propagating waves are multi-modal and interact with discontinuities differently, increasing complexity and leading to different response signals. When the researcher wants to gain insight into the behavior of guided waves, predicting response signals for different combinations of modes becomes necessary. However, the task can become computationally costly when physics-based models are used. Digital twins can enable a practitioner to deal systematically with the complexities of guided wave monitoring in practical or user-specified settings. This paper investigates the use of a hybrid digital model of an operational rail track to predict response signals for varying user-specified settings, specifically, the prediction of response signals for various combinations of modes of propagation in the rail. The digital twin hybrid model employs a physics-based model and a data-driven model. The physics-based model simulates the wave propagation response using techniques developed from the traditional 3D finite element method and the 2D semi-analytical finite element method (FEM). The physics-based model is used to generate virtual experimental signals containing different combinations of modes of propagation. These response signals are used to train the data-driven model based on a variational auto-encoder (VAE). Given an input baseline signal containing only the most dominant mode excited by a transducer, the VAE is trained to predict an inspection signal with increased complexity according to the specified combination of modes. The results show that, once the VAE has been trained, it can be used to predict inspection signals for different combinations of propagating modes, thus replacing the physics-based model, which is computationally costly. In the future, the VAE architecture will be adapted to predict response signals for varying environmental and operational conditions. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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15 pages, 4951 KiB

Open AccessArticle

Spatio-Temporal Gradient Enhanced Surrogate Modeling Strategies

by Johann M. Bouwer, Daniel N. Wilke and Schalk Kok

Math. Comput. Appl. 2023, 28(2), 57; https://doi.org/10.3390/mca28020057 - 8 Apr 2023

Cited by 1 | Viewed by 2084

Abstract

This research compares the performance of space-time surrogate models (STSMs) and network surrogate models (NSMs). Specifically, when the system response varies over time (or pseudo-time), the surrogates must predict the system response. A surrogate model is used to approximate the response of computationally [...] Read more.

This research compares the performance of space-time surrogate models (STSMs) and network surrogate models (NSMs). Specifically, when the system response varies over time (or pseudo-time), the surrogates must predict the system response. A surrogate model is used to approximate the response of computationally expensive spatial and temporal fields resulting from some computational mechanics simulations. Within a design context, a surrogate takes a vector of design variables that describe a current design and returns an approximation of the design’s response through a pseudo-time variable. To compare various radial basis function (RBF) surrogate modeling approaches, the prediction of a load displacement path of a snap-through structure is used as an example numerical problem. This work specifically considers the scenario where analytical sensitivities are available directly from the computational mechanics’ solver and therefore gradient enhanced surrogates are constructed. In addition, the gradients are used to perform a domain transformation preprocessing step to construct surrogate models in a more isotropic domain, which is conducive to RBFs. This work demonstrates that although the gradient-based domain transformation scheme offers a significant improvement to the performance of the space-time surrogate models (STSMs), the network surrogate model (NSM) is far more robust. This research offers explanations for the improved performance of NSMs over STSMs and recommends future research to improve the performance of STSMs. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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20 pages, 5672 KiB

Open AccessArticle

Fourier Image Analysis of Multiphase Interfaces to Quantify Primary Atomization

by Johannes C. Joubert, Daniel N. Wilke and Patrick Pizette

Math. Comput. Appl. 2023, 28(2), 55; https://doi.org/10.3390/mca28020055 - 3 Apr 2023

Cited by 2 | Viewed by 1900

Abstract

This work describes a post-processing scheme for multiphase flow systems to characterize primary atomization. The scheme relies on the 2D fast Fourier transform (FFT) to separate the inherently multi-scale features present in the flow results. Emphasis is put on the robust quantitative analysis [...] Read more.

This work describes a post-processing scheme for multiphase flow systems to characterize primary atomization. The scheme relies on the 2D fast Fourier transform (FFT) to separate the inherently multi-scale features present in the flow results. Emphasis is put on the robust quantitative analysis enabled by this scheme, with this work specifically focusing on comparing atomizer nozzle designs. The generalized finite difference (GFD) method is used to simulate a high pressure gas injected into a viscous liquid stream. The proposed scheme is applied to time-averaged results exclusively. The scheme is used to evaluate both the surface and volume features of the fluid system. Due to the better recovery of small-scale features using the proposed scheme, the benefits of post-processing multiphase surface information rather than fluid volume information was shown. While the volume information lacks the fine-scale details of the surface information, the duality between interfaces and fluid volumes leads to similar trends related to the large-scale spatial structure recovered from both surface- and volume-based data sets. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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17 pages, 10213 KiB

Open AccessArticle

Generative Design of Soft Robot Actuators Using ESP

by Martin Philip Venter and Izak Johannes Joubert

Math. Comput. Appl. 2023, 28(2), 53; https://doi.org/10.3390/mca28020053 - 3 Apr 2023

Cited by 4 | Viewed by 2674

Abstract

Soft robotics is an emerging field that leverages the compliant nature of materials to control shape and behaviour. However, designing soft robots presents a challenge, as they do not have discrete points of articulation and instead articulate through deformation in whole regions of [...] Read more.

Soft robotics is an emerging field that leverages the compliant nature of materials to control shape and behaviour. However, designing soft robots presents a challenge, as they do not have discrete points of articulation and instead articulate through deformation in whole regions of the robot. This results in a vast, unexplored design space with few established design methods. This paper presents a practical generative design process that combines the Encapsulation, Syllabus, and Pandamonium method with a reduced-order model to produce results comparable to the existing state-of-the-art in reduced design time while including the human designer meaningfully in the design process and facilitating the inclusion of other numerical techniques such as Markov chain Monte Carlo methods. Using a combination of reduced-order models, L-systems, MCMC, curve matching, and optimisation, we demonstrate that our method can produce functional 2D articulating soft robot designs in less than 1 s, a significant reduction in design time compared to monolithic methods, which can take several days. Additionally, we qualitatively show how to extend our approach to produce more complex 3D robots, such as an articulating tentacle with multiple grippers. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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17 pages, 3766 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A PINN Surrogate Modeling Methodology for Steady-State Integrated Thermofluid Systems Modeling

by Kristina Laugksch, Pieter Rousseau and Ryno Laubscher

Math. Comput. Appl. 2023, 28(2), 52; https://doi.org/10.3390/mca28020052 - 27 Mar 2023

Cited by 2 | Viewed by 3408

Abstract

Physics-informed neural networks (PINNs) were developed to overcome the limitations associated with the acquisition of large training data sets that are commonly encountered when using purely data-driven machine learning methods. This paper proposes a PINN surrogate modeling methodology for steady-state integrated thermofluid systems [...] Read more.

Physics-informed neural networks (PINNs) were developed to overcome the limitations associated with the acquisition of large training data sets that are commonly encountered when using purely data-driven machine learning methods. This paper proposes a PINN surrogate modeling methodology for steady-state integrated thermofluid systems modeling based on the mass, energy, and momentum balance equations, combined with the relevant component characteristics and fluid property relationships. The methodology is applied to two thermofluid systems that encapsulate the important phenomena typically encountered, namely: (i) a heat exchanger network with two different fluid streams and components linked in series and parallel; and (ii) a recuperated closed Brayton cycle with various turbomachines and heat exchangers. The results generated with the PINN models were compared to benchmark solutions generated via conventional, physics-based thermofluid process models. The largest average relative errors are 0.17% and 0.93% for the heat exchanger network and Brayton cycle, respectively. It was shown that the use of a hybrid Adam-TNC optimizer requires between 180 and 690 fewer iterations during the training process, thus providing a significant computational advantage over a pure Adam optimization approach. The resulting PINN models can make predictions 75 to 88 times faster than their respective conventional process models. This highlights the potential for PINN surrogate models as a valuable engineering tool in component and system design and optimization, as well as in real-time simulation for anomaly detection, diagnosis, and forecasting. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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22 pages, 3475 KiB

Open AccessArticle

A Generalized Finite Difference Scheme for Multiphase Flow

by Johannes C. Joubert, Daniel N. Wilke and Patrick Pizette

Math. Comput. Appl. 2023, 28(2), 51; https://doi.org/10.3390/mca28020051 - 26 Mar 2023

Cited by 2 | Viewed by 2484

Abstract

This paper presents a GPU-based, incompressible, multiphase generalized finite difference solver for simulating multiphase flow. The method includes a dampening scheme that allows for large density ratio cases to be simulated. Two verification studies are performed by simulating the relaxation of a square [...] Read more.

This paper presents a GPU-based, incompressible, multiphase generalized finite difference solver for simulating multiphase flow. The method includes a dampening scheme that allows for large density ratio cases to be simulated. Two verification studies are performed by simulating the relaxation of a square droplet surrounded by a light fluid and a bubble rising in a denser fluid. The scheme is also used to simulate the collision of binary droplets at moderate Reynolds numbers (250–550). The effects of the surface tension and density ratio are explored in this work by considering cases with Weber numbers of 8 and 180 and density ratios of 2:1 and 1000:1. The robustness of the multiphase scheme is highlighted when resolving thin fluid structures arising in both high and low density ratio cases at We = 180. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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14 pages, 3663 KiB

Open AccessArticle

Numerical Analysis of the Effect of the Vortex Finder on the Hydrocyclone’s Split Water Ratio and Separation Performance

by Vuyo T. Hashe and Thokozani J. Kunene

Math. Comput. Appl. 2023, 28(2), 50; https://doi.org/10.3390/mca28020050 - 22 Mar 2023

Cited by 1 | Viewed by 2285

Abstract

Hydrocyclones are devices used in numerous areas of the chemical, food, and mineral industries to separate fine particles. A hydrocyclone with a diameter of d50 mm was modeled using the commercial Simcenter STAR-CCM+13 computational fluid dynamics (CFD) simulation package. The numerical methods [...] Read more.

Hydrocyclones are devices used in numerous areas of the chemical, food, and mineral industries to separate fine particles. A hydrocyclone with a diameter of d50 mm was modeled using the commercial Simcenter STAR-CCM+13 computational fluid dynamics (CFD) simulation package. The numerical methods confirmed the results of the different parameters, such as the properties of the volume fraction, based on CFD simulations. Reynolds Stress Model (RSM) and the combined technique of volume of fluid (VOF) and discrete element model (DEM) for water and air models were selected to evaluate semi-implicit pressure-linked equations and combine the momentum with continuity laws to obtain derivatives of the pressure. The targeted particle sizes were in a range of 8–100 microns for a dewatering application. The depth of the vortex finder was varied to 20 mm, 30 mm, and 35 mm to observe the effects of pressure drop and separation efficiency. The split water ratio increased toward a 50% split of overflow and underflow rates as the length of the vortex finder increased. It results in better particle separation when there is a high injection rate at the inlet. The tangential and axial velocities increased as the vortex finder length increased. As the depth of the vortex finder length increased, the time for particle re-entrainment into the underflow stream increased, and the separation efficiency improved. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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12 pages, 1763 KiB

Open AccessArticle

A Hierarchical Design Framework for the Design of Soft Robots

by Philip Frederik Ligthart and Martin Philip Venter

Math. Comput. Appl. 2023, 28(2), 47; https://doi.org/10.3390/mca28020047 - 21 Mar 2023

Cited by 1 | Viewed by 2683

Abstract

This paper demonstrates the effectiveness of a hierarchical design framework in developing environment-specific behaviour for fluid-actuated soft robots. Our proposed framework employs multi-step optimisation and reduced-order modelling to reduce the computational expense associated with simulating non-linear materials used in the design process. Specifically, [...] Read more.

This paper demonstrates the effectiveness of a hierarchical design framework in developing environment-specific behaviour for fluid-actuated soft robots. Our proposed framework employs multi-step optimisation and reduced-order modelling to reduce the computational expense associated with simulating non-linear materials used in the design process. Specifically, our framework requires the designer to make high-level decisions to simplify the optimisations, targeting simple objectives in earlier steps and more complex objectives in later steps. We present a case study, where our proposed framework is compared to a conventional direct design approach for a simple 2D design. A soft pneumatic bending actuator was designed that is able to perform asymmetrical motion when actuated cyclically. Our results show that the hierarchical framework can find almost 2.5 times better solutions in less than 3% of the time when compared to a direct design approach. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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19 pages, 2211 KiB

Open AccessArticle

An Analysis of Numerical Homogenisation Methods Applied on Corrugated Paperboard

by Rhoda Ngira Aduke, Martin P. Venter and Corné J. Coetzee

Math. Comput. Appl. 2023, 28(2), 46; https://doi.org/10.3390/mca28020046 - 20 Mar 2023

Cited by 2 | Viewed by 2563

Abstract

Corrugated paperboard is a sandwich structure composed of wavy paper (fluting) bonded between two flat paper sheets (liners). The analysis of an entire package using three-dimensional numerical finite element models is computationally expensive due to the waved geometry of the board that requires [...] Read more.

Corrugated paperboard is a sandwich structure composed of wavy paper (fluting) bonded between two flat paper sheets (liners). The analysis of an entire package using three-dimensional numerical finite element models is computationally expensive due to the waved geometry of the board that requires the use of a relatively large number of elements in a simulation. Because of this, homogenisation approaches are used to evaluate equivalent homogenous models with similar material properties. These techniques have been successfully implemented by various researchers to evaluate the strength of corrugated paperboard. However, studies analysing the various homogenisation techniques and their ranges of applicability are limited. This study analyses the application of three homogenisation techniques: classical laminate plate theory, first-order shear deformation theory and deformation energy equivalence method in the evaluation of effective elastic material properties. In addition, inverse analysis has been applied to determine the effective properties of the board. Finite element models have been used to evaluate the accuracy of the three homogenisation techniques in comparison to the inverse method in modelling four-point bending tests and the results reported. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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17 pages, 6288 KiB

Open AccessArticle

CFD Modelling of Gas-Solid Reactions: Analysis of Iron and Manganese Oxides Reduction with Hydrogen

by Mopeli Khama and Quinn Reynolds

Math. Comput. Appl. 2023, 28(2), 43; https://doi.org/10.3390/mca28020043 - 18 Mar 2023

Viewed by 2748

Abstract

Metallurgical processes are characterized by a complex interplay of heat and mass transfer, momentum transfer, and reaction kinetics, and these interactions play a crucial role in reactor performance. Integrating chemistry and transport results in stiff and non-linear equations and longer time and length [...] Read more.

Metallurgical processes are characterized by a complex interplay of heat and mass transfer, momentum transfer, and reaction kinetics, and these interactions play a crucial role in reactor performance. Integrating chemistry and transport results in stiff and non-linear equations and longer time and length scales, which ultimately leads to a high computational expense. The current study employs the OpenFOAM solver based on a fictitious domain method to analyze gas-solid reactions in a porous medium using hydrogen as a reducing agent. The reduction of oxides with hydrogen involves the hierarchical phenomena that influence the reaction rates at various temporal and spatial scales; thus, multi-scale models are needed to bridge the length scale from micro-scale to macro-scale accurately. As a first step towards developing such capabilities, the current study analyses OpenFOAM reacting flow methods in cases related to hydrogen reduction of iron and manganese oxides. Since reduction of the oxides of interest with hydrogen requires significant modifications to the current industrial processes, this model can aid in the design and optimization. The model was verified against experimental data and the dynamic features of the porous medium observed as the reaction progresses is well captured by the model. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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15 pages, 6200 KiB

Open AccessArticle

Numerical Modeling of Cavitation Rates and Noise Acoustics of Marine Propellers

by Kwanda Mercury Dlamini, Vuyo Terrence Hashe and Thokozani Justin Kunene

Math. Comput. Appl. 2023, 28(2), 42; https://doi.org/10.3390/mca28020042 - 15 Mar 2023

Cited by 5 | Viewed by 3179

Abstract

The study numerically investigated the noise dissipation, cavitation, output power, and energy produced by marine propellers. A Ffowcs Williams–Hawkings (FW–H) model was used to determine the effects of three different marine propellers with three to five blades and a fixed advancing ratio. The [...] Read more.

The study numerically investigated the noise dissipation, cavitation, output power, and energy produced by marine propellers. A Ffowcs Williams–Hawkings (FW–H) model was used to determine the effects of three different marine propellers with three to five blades and a fixed advancing ratio. The large-eddy Simulations model best predicted the turbulent structures’ spatial and temporal variation, which would better illustrate the flow physics. It was found that a high angle of incidence between the blade’s leading edge and the water flow direction typically causes the hub vortex to cavitate. The roll-up of the cavitating tip vortex was closely related to propeller noise. The five-blade propeller was quieter under the same dynamic conditions, such as the advancing ratio, compared to three- or four-blade propellers. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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18 pages, 11533 KiB

Open AccessArticle

A Strain-Gauge-Based Method for the Compensation of Out-of-Plane Motions in 2D Digital Image Correlation

by Carl-Hein Visser, Gerhard Venter and Melody Neaves

Math. Comput. Appl. 2023, 28(2), 40; https://doi.org/10.3390/mca28020040 - 10 Mar 2023

Cited by 2 | Viewed by 2317

Abstract

When performing a digital image correlation (DIC) measurement, multi-camera stereo-DIC is generally preferred over single-camera 2D-DIC. Unlike 2D-DIC, stereo-DIC is able to minimise the in-plane strain error that results from out-of-plane motion. This makes 2D-DIC a less viable alternative for strain measurements than [...] Read more.

When performing a digital image correlation (DIC) measurement, multi-camera stereo-DIC is generally preferred over single-camera 2D-DIC. Unlike 2D-DIC, stereo-DIC is able to minimise the in-plane strain error that results from out-of-plane motion. This makes 2D-DIC a less viable alternative for strain measurements than stereo-DIC, despite being less financially and computationally expensive. This work, therefore, proposes a strain-gauge-based method for the compensation of errors from out-of-plane motion in 2D-DIC strain measurements on planar specimens. The method was first developed using equations for the theoretical strain error from out-of-plane motions in 2D-DIC and was then applied experimentally in tensile tests to two different dog-bone specimen geometries. The compensation method resulted in a clear reduction in the strain error in 2D-DIC. The strain-gauge-based method thus improves the accuracy of a 2D-DIC measurement, making it a more viable option for performing full-field strain measurements and providing a possible alternative in cases where stereo-DIC is not practical or is unavailable. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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12 pages, 1560 KiB

Open AccessArticle

Construction and Modification of Topological Tables for Digital Models of Linear Complexes

by Aleksandr N. Rozhkov and Vera V. Galishnikova

Math. Comput. Appl. 2023, 28(2), 37; https://doi.org/10.3390/mca28020037 - 7 Mar 2023

Viewed by 1627

Abstract

Building information systems use topological tables to implement the transition from two-dimensional line drawings of the geometry of buildings to digital three-dimensional models of linear complexes. The topological elements of the complex are named and the topological relations of the complex are described [...] Read more.

Building information systems use topological tables to implement the transition from two-dimensional line drawings of the geometry of buildings to digital three-dimensional models of linear complexes. The topological elements of the complex are named and the topological relations of the complex are described by arranging the element names in topological tables. The efficient construction and modification of topological tables for complete buildings is investigated. The topology of a linear complex with nodes, edges, faces, and cells is described with 12 tables. Three of the tables of a complex are independent of each other and form a basis for the construction of the other tables. A highly efficient construction algorithm with complexity O (number of cells) for typical buildings with an approximately constant number of edges per face and faces per cell of is presented. In practice, building designs and their digital models are frequently modified. A modification algorithm is presented, whose complexity equals that of the construction algorithm. Examples illustrate that the efficient algorithms permit the replacement of the conventional focus on the topology of building components by a focus on the topology of the entire building. A set of properties of the original, which are not explicitly described by the topological tables, for example, the orientation of surfaces and multiply connected domains, are analyzed in the paper. An overview of the research dealing with the topological attributes that are not contained in topological tables concludes the paper. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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18 pages, 430 KiB

Open AccessArticle

Treatment Effect Performance of the X-Learner in the Presence of Confounding and Non-Linearity

by Bevan I. Smith, Charles Chimedza and Jacoba H. Bührmann

Math. Comput. Appl. 2023, 28(2), 32; https://doi.org/10.3390/mca28020032 - 27 Feb 2023

Cited by 1 | Viewed by 3153

Abstract

This study critically evaluates a recent machine learning method called the X-Learner, that aims to estimate treatment effects by predicting counterfactual quantities. It uses information from the treated group to predict counterfactuals for the control group and vice versa. The problem is that [...] Read more.

This study critically evaluates a recent machine learning method called the X-Learner, that aims to estimate treatment effects by predicting counterfactual quantities. It uses information from the treated group to predict counterfactuals for the control group and vice versa. The problem is that studies have either only been applied to real world data without knowing the ground truth treatment effects, or have not been compared with the traditional regression methods for estimating treatment effects. This study therefore critically evaluates this method by simulating various scenarios that include observed confounding and non-linearity in the data. Although the regression X-Learner performs just as well as the traditional regression model, the other base learners performed worse. Additionally, when non-linearity was introduced into the data, the results of the X-Learner became inaccurate. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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24 pages, 9994 KiB

Open AccessArticle

Experimental and Numerical Investigation of the In-Plane Compression of Corrugated Paperboard Panels

by Johan Cillie and Corné Coetzee

Math. Comput. Appl. 2022, 27(6), 108; https://doi.org/10.3390/mca27060108 - 12 Dec 2022

Cited by 9 | Viewed by 2719

Abstract

Finite element analysis (FEA) has been proven as a useful design tool to model corrugated paperboard boxes, and is capable of accurately predicting load capacity. The in-plane deformation, however, is usually significantly underpredicted. To investigate this discrepancy, a panel compression test jig, that [...] Read more.

Finite element analysis (FEA) has been proven as a useful design tool to model corrugated paperboard boxes, and is capable of accurately predicting load capacity. The in-plane deformation, however, is usually significantly underpredicted. To investigate this discrepancy, a panel compression test jig, that implemented simply supported boundary conditions, was built to test individual panels. The panels were then modelled using non-linear FEA with a linear material model. The results show that the in-plane deformation was still underpredicted, but a general improvement was seen. Three discrepancies were identified. The first was that the panels showed an initial region of low stiffness that was not present in the FEA results. This was attributed to imperfections in the panels and jig. Secondly, the experimental results reported a lower stiffness than the FEA. Applying an initial imperfection in the shape of the first buckling mode shape was found to reduce the FEA stiffness. Thirdly, the panels showed a decrease in stiffness near failure, which was not seen in the FEA. A bi-linear material model was investigated and holds the potential to improve the results. Box compression tests were performed on a Regular Slotted Container (RSC) with the same dimensions as the tested panel. The box displaced 13.1 mm compared to 3.5 mm for the panel. There was an initial region of low stiffness, which accounted for 7 mm of displacement compared to 0.5 mm for the panels. Thus, box complexities such as horizontal creases should be included in finite element (FE) models to accurately predict the in-plane deformation, while a bi-linear (or any other non-linear) material model may be useful for panel compression. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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22 pages, 14309 KiB

Open AccessArticle

The Modification of the Dynamic Behaviour of the Cyclonic Flow in a Hydrocyclone under Surging Conditions

by Muaaz Bhamjee, Simon H. Connell and André Leon Nel

Math. Comput. Appl. 2022, 27(6), 88; https://doi.org/10.3390/mca27060088 - 22 Oct 2022

Viewed by 2227

Abstract

The aim in this study was to determine how surging modifies the dynamic behaviour of the cyclonic flow in a hydrocyclone using computational fluid and granular dynamics models. The Volume-of-Fluid model was used to model the air-core formation. Fluid–particle, particle–particle, and particle–wall interactions [...] Read more.

The aim in this study was to determine how surging modifies the dynamic behaviour of the cyclonic flow in a hydrocyclone using computational fluid and granular dynamics models. The Volume-of-Fluid model was used to model the air-core formation. Fluid–particle, particle–particle, and particle–wall interactions were modelled using an unsteady two-way coupled Discrete Element Method. Turbulence was modelled using both the Reynold’s Stress Model and the Large Eddy Simulation. The model predictions indicate that the phenomenon of surging modifies the dynamics of the cyclonic flow in hydrocyclones and subsequently impacts separation. The results reveal that the primary cyclonic separation mechanisms break down during surging and result in air-core suppression. The flow and primary separation mechanism in the core of the hydrocyclone is driven by the pressure drop and the flow and primary separation mechanism near the wall is primarily driven by the gravitational and centrifugal force-induced momentum. However, surging causes a breakdown in this mechanism by swapping this primary flow and separation behaviour, where the pressure drop becomes the primary driver of the flow near the walls and gravitational and centrifugal force-induced momentum primarily drives the flow in the core of the hydrocyclone. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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16 pages, 1064 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Comparison of Two Aspects of a PDE Model for Biological Network Formation

by Clarissa Astuto, Daniele Boffi, Jan Haskovec, Peter Markowich and Giovanni Russo

Math. Comput. Appl. 2022, 27(5), 87; https://doi.org/10.3390/mca27050087 - 17 Oct 2022

Cited by 3 | Viewed by 2423

Abstract

We compare the solutions of two systems of partial differential equations (PDEs), seen as two different interpretations of the same model which describes the formation of complex biological networks. Both approaches take into account the time evolution of the medium flowing through the [...] Read more.

We compare the solutions of two systems of partial differential equations (PDEs), seen as two different interpretations of the same model which describes the formation of complex biological networks. Both approaches take into account the time evolution of the medium flowing through the network, and we compute the solution of an elliptic–parabolic PDE system for the conductivity vector m, the conductivity tensor

C

and the pressure p. We use finite differences schemes in a uniform Cartesian grid in a spatially two-dimensional setting to solve the two systems, where the parabolic equation is solved using a semi-implicit scheme in time. Since the conductivity vector and tensor also appear in the Poisson equation for the pressure p, the elliptic equation depends implicitly on time. For this reason, we compute the solution of three linear systems in the case of the conductivity vector

m \in R^{2}

and four linear systems in the case of the symmetric conductivity tensor

C \in R^{2 \times 2}

at each time step. To accelerate the simulations, we make use of the Alternating Direction Implicit (ADI) method. The role of the parameters is important for obtaining detailed solutions. We provide numerous tests with various values of the parameters involved to determine the differences in the solutions of the two systems. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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17 pages, 17738 KiB

Open AccessArticle

Estimation of Pulmonary Arterial Pressure Using Simulated Non-Invasive Measurements and Gradient-Based Optimization Techniques

by Ryno Laubscher, Johan Van Der Merwe, Philip G. Herbst and Jacques Liebenberg

Math. Comput. Appl. 2022, 27(5), 83; https://doi.org/10.3390/mca27050083 - 28 Sep 2022

Cited by 2 | Viewed by 2424

Abstract

Reliable quantification of pulmonary arterial pressure is essential in the diagnostic and prognostic assessment of a range of cardiovascular pathologies, including rheumatic heart disease, yet an accurate and routinely available method for its quantification remains elusive. This work proposes an approach to infer [...] Read more.

Reliable quantification of pulmonary arterial pressure is essential in the diagnostic and prognostic assessment of a range of cardiovascular pathologies, including rheumatic heart disease, yet an accurate and routinely available method for its quantification remains elusive. This work proposes an approach to infer pulmonary arterial pressure based on scientific machine learning techniques and non-invasive, clinically available measurements. A 0D multicompartment model of the cardiovascular system was optimized using several optimization algorithms subject to forward-mode automatic differentiation. Measurement data were synthesized from known parameters to represent the healthy, mitral regurgitant, aortic stenosed, and combined valvular disease situations with and without pulmonary hypertension. Eleven model parameters were selected for optimization based on 95% explained variation in mean pulmonary arterial pressure. A hybrid Adam and limited-memory Broyden–Fletcher–Goldfarb–Shanno optimizer yielded the best results with input data including valvular flow rates, heart chamber volume changes, and systematic arterial pressure. Mean absolute percentage errors ranged from 1.8% to 3.78% over the simulated test cases. The model was able to capture pressure dynamics under hypertensive conditions with pulmonary arterial systole, diastole, and mean pressure average percentage errors of 1.12%, 2.49%, and 2.14%, respectively. The low errors highlight the potential of the proposed model to determine pulmonary pressure for diseased heart valves and pulmonary hypertensive conditions. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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14 pages, 1247 KiB

Open AccessArticle

Area of the Intersection between a Sphere and a Cylindrical Plane

by Charl Gabriël Du Toit

Math. Comput. Appl. 2022, 27(5), 79; https://doi.org/10.3390/mca27050079 - 16 Sep 2022

Cited by 1 | Viewed by 2279

Abstract

A proper understanding of the porous structure of packed beds of spheres is imperative in the analysis and design of the processes involving fluid flow and heat and mass transfer. The radial variation in porosity is of specific interest. When the positions and [...] Read more.

A proper understanding of the porous structure of packed beds of spheres is imperative in the analysis and design of the processes involving fluid flow and heat and mass transfer. The radial variation in porosity is of specific interest. When the positions and sizes of the spheres are known, the radial variation in porosity can be determined using volume-based, area-based, or line-based approaches. Here, the focus is on the area-based methods which employ the intersections between the spheres and selected cylindrical planes to determine the radial variation in porosity, focusing specifically on the calculation of the area of the curved elliptic intersection between a sphere and a cylindrical plane. Using geometrical considerations, analytical integral expressions have been derived based on the axial direction, angular direction, or the radial direction as independent variables. The integral expressions cannot be integrated analytically and have been evaluated using approximations or numerical integration. However, only indirect validation of the calculation of the intersection area has been provided by comparing the radial porosity profiles obtained with experimental data. This study provides direct validation of the calculated area through refined numerical integration of the primary integral expressions and the evaluation of the area employing computer-aided design software. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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