Open AccessReview
Molecular Dynamics Simulation of High Density DNA Arrays
Computation 2018, 6(1), 3; doi:10.3390/computation6010003 -
Abstract
Densely packed DNA arrays exhibit hexagonal and orthorhombic local packings, as well as a weakly first order transition between them. While we have some understanding of the interactions between DNA molecules in aqueous ionic solutions, the structural details of its ordered phases and
[...] Read more.
Densely packed DNA arrays exhibit hexagonal and orthorhombic local packings, as well as a weakly first order transition between them. While we have some understanding of the interactions between DNA molecules in aqueous ionic solutions, the structural details of its ordered phases and the mechanism governing the respective phase transitions between them remains less well understood. Since at high DNA densities, i.e., small interaxial spacings, one can neither neglect the atomic details of the interacting macromolecular surfaces nor the atomic details of the intervening ionic solution, the atomistic resolution is a sine qua non to properly describe and analyze the interactions between DNA molecules. In fact, in order to properly understand the details of the observed osmotic equation of state, one needs to implement multiple levels of organization, spanning the range from the molecular order of DNA itself, the possible ordering of counterions, and then all the way to the induced molecular ordering of the aqueous solvent, all coupled together by electrostatic, steric, thermal and direct hydrogen-bonding interactions. Multiscale simulations therefore appear as singularly suited to connect the microscopic details of this system with its macroscopic thermodynamic behavior. We review the details of the simulation of dense atomistically resolved DNA arrays with different packing symmetries and the ensuing osmotic equation of state obtained by enclosing a DNA array in a monovalent salt and multivalent (spermidine) counterions within a solvent permeable membrane, mimicking the behavior of DNA arrays subjected to external osmotic stress. By varying the DNA density, the local packing symmetry, and the counterion type, we are able to analyze the osmotic equation of state together with the full structural characterization of the DNA subphase, the counterion distribution and the solvent structural order in terms of its different order parameters and consequently identify the most important contribution to the DNA-DNA interactions at high DNA densities. Full article
Figures

Open AccessArticle
Temporal Variation of the Pressure from a Steady Impinging Jet Model of Dry Microburst-Like Wind Using URANS
Computation 2018, 6(1), 2; doi:10.3390/computation6010002 -
Abstract
The objective of this study is to investigate the temporal behavior of the pressure field of a stationary dry microburst-like wind phenomenon utilizing Unsteady Reynolds-averaged Navier-Stokes (URANS) numerical simulations. Using an axisymmetric steady impinging jet model, the dry microburst-like wind is simulated from
[...] Read more.
The objective of this study is to investigate the temporal behavior of the pressure field of a stationary dry microburst-like wind phenomenon utilizing Unsteady Reynolds-averaged Navier-Stokes (URANS) numerical simulations. Using an axisymmetric steady impinging jet model, the dry microburst-like wind is simulated from the initial release of a steady downdraft flow, till the time after the primary vortices have fully convected out of the stagnation region. The validated URANS results presented herein shed light on the temporal variation of the pressure field which is in agreement with the qualitative description obtained from field measurements. The results have an impact on understanding the wind load on structures from the initial touch-down phase of the downdraft from a microburst. The investigation is based on CFD techniques, together with a simple impinging jet model that does not include any microphysical processes. Unlike previous investigations, this study focuses on the transient pressure field from a downdraft without obstacles. Full article
Figures

Figure 1

Open AccessArticle
Developing Computational Geometry and Network Graph Models of Human Lymphatic System
Computation 2018, 6(1), 1; doi:10.3390/computation6010001 -
Abstract
The lymphatic system is a body-wide network of lymphatic vessels and lymphoid organs. The complexity of the structural and functional organization of the lymphatic system implies the necessity of using computational modeling approaches to unravel the mechanisms of its regulation in quantitative terms.
[...] Read more.
The lymphatic system is a body-wide network of lymphatic vessels and lymphoid organs. The complexity of the structural and functional organization of the lymphatic system implies the necessity of using computational modeling approaches to unravel the mechanisms of its regulation in quantitative terms. Although it is a vital part of the circulatory and immune systems, the lymphatic system remains poorly investigated as a mathematical modeling object. Modeling of the lymphatic vessel network needs to be established using a systematic approach in order to advance the model-driven research of this important physiological system. In our study, we elucidate key general features underlying the 3D structural organization of the lymphatic system in order to develop computational geometry and network graph models of the human lymphatic system based on available anatomical data (from the PlasticBoy project), which provides an estimate of the structure of the lymphatic system, and to analyze the topological properties of the resulting models. Full article
Figures

Figure 1

Open AccessFeature PaperReview
Challenges for Theory and Computation
Computation 2017, 5(4), 49; doi:10.3390/computation5040049 -
Abstract
The routinely made assumptions for simulating solid materials are briefly summarized, since they need to be critically assessed when new aspects become important, such as excited states, finite temperature, time-dependence, etc. The significantly higher computer power combined with improved experimental data open new
[...] Read more.
The routinely made assumptions for simulating solid materials are briefly summarized, since they need to be critically assessed when new aspects become important, such as excited states, finite temperature, time-dependence, etc. The significantly higher computer power combined with improved experimental data open new areas for interdisciplinary research, for which new ideas and concepts are needed. Full article
Open AccessArticle
Nonlinear-Adaptive Mathematical System Identification
Computation 2017, 5(4), 47; doi:10.3390/computation5040047 -
Abstract
By reversing paradigms that normally utilize mathematical models as the basis for nonlinear adaptive controllers, this article describes using the controller to serve as a novel computational approach for mathematical system identification. System identification usually begins with the dynamics, and then seeks to
[...] Read more.
By reversing paradigms that normally utilize mathematical models as the basis for nonlinear adaptive controllers, this article describes using the controller to serve as a novel computational approach for mathematical system identification. System identification usually begins with the dynamics, and then seeks to parameterize the mathematical model in an optimization relationship that produces estimates of the parameters that minimize a designated cost function. The proposed methodology uses a DC motor with a minimum-phase mathematical model controlled by a self-tuning regulator without model pole cancelation. The normal system identification process is briefly articulated by parameterizing the system for least squares estimation that includes an allowance for exponential forgetting to deal with time-varying plants. Next, towards the proposed approach, the Diophantine equation is derived for an indirect self-tuner where feedforward and feedback controls are both parameterized in terms of the motor’s math model. As the controller seeks to nullify tracking errors, the assumed plant parameters are adapted and quickly converge on the correct parameters of the motor’s math model. Next, a more challenging non-minimum phase system is investigated, and the earlier implemented technique is modified utilizing a direct self-tuner with an increased pole excess. The nominal method experiences control chattering (an undesirable characteristic that could potentially damage the motor during testing), while the increased pole excess eliminates the control chattering, yet maintains effective mathematical system identification. This novel approach permits algorithms normally used for control to instead be used effectively for mathematical system identification. Full article
Figures

Figure 1

Open AccessArticle
A Holistic Scalable Implementation Approach of the Lattice Boltzmann Method for CPU/GPU Heterogeneous Clusters
Computation 2017, 5(4), 48; doi:10.3390/computation5040048 -
Abstract
Heterogeneous clusters are a widely utilized class of supercomputers assembled from different types of computing devices, for instance CPUs and GPUs, providing a huge computational potential. Programming them in a scalable way exploiting the maximal performance introduces numerous challenges such as optimizations for
[...] Read more.
Heterogeneous clusters are a widely utilized class of supercomputers assembled from different types of computing devices, for instance CPUs and GPUs, providing a huge computational potential. Programming them in a scalable way exploiting the maximal performance introduces numerous challenges such as optimizations for different computing devices, dealing with multiple levels of parallelism, the application of different programming models, work distribution, and hiding of communication with computation. We utilize the lattice Boltzmann method for fluid flow as a representative of a scientific computing application and develop a holistic implementation for large-scale CPU/GPU heterogeneous clusters. We review and combine a set of best practices and techniques ranging from optimizations for the particular computing devices to the orchestration of tens of thousands of CPU cores and thousands of GPUs. Eventually, we come up with an implementation using all the available computational resources for the lattice Boltzmann method operators. Our approach shows excellent scalability behavior making it future-proof for heterogeneous clusters of the upcoming architectures on the exaFLOPS scale. Parallel efficiencies of more than 90% are achieved leading to 2604.72 GLUPS utilizing 24,576 CPU cores and 2048 GPUs of the CPU/GPU heterogeneous cluster Piz Daint and computing more than 6.8×109 lattice cells. Full article
Figures

Figure 1

Open AccessFeature PaperReview
Dynamic Data-Driven Modeling for Ex Vivo Data Analysis: Insights into Liver Transplantation and Pathobiology
Computation 2017, 5(4), 46; doi:10.3390/computation5040046 -
Abstract
Extracorporeal organ perfusion, in which organs are preserved in an isolated, ex vivo environment over an extended time-span, is a concept that has led to the development of numerous alternative preservation protocols designed to better maintain organ viability prior to transplantation. These protocols
[...] Read more.
Extracorporeal organ perfusion, in which organs are preserved in an isolated, ex vivo environment over an extended time-span, is a concept that has led to the development of numerous alternative preservation protocols designed to better maintain organ viability prior to transplantation. These protocols offer researchers a novel opportunity to obtain extensive sampling of isolated organs, free from systemic influences. Data-driven computational modeling is a primary means of integrating the extensive and multivariate data obtained in this fashion. In this review, we focus on the application of dynamic data-driven computational modeling to liver pathophysiology and transplantation based on data obtained from ex vivo organ perfusion. Full article
Figures

Figure 1

Open AccessArticle
Deformable Cell Model of Tissue Growth
Computation 2017, 5(4), 45; doi:10.3390/computation5040045 -
Abstract
This paper is devoted to modelling tissue growth with a deformable cell model. Each cell represents a polygon with particles located at its vertices. Stretching, bending and pressure forces act on particles and determine their displacement. Pressure-dependent cell proliferation is considered. Various patterns
[...] Read more.
This paper is devoted to modelling tissue growth with a deformable cell model. Each cell represents a polygon with particles located at its vertices. Stretching, bending and pressure forces act on particles and determine their displacement. Pressure-dependent cell proliferation is considered. Various patterns of growing tissue are observed. An application of the model to tissue regeneration is illustrated. Approximate analytical models of tissue growth are developed. Full article
Figures

Figure 1

Open AccessArticle
Multiresolution Modeling of Semidilute Polymer Solutions: Coarse-Graining Using Wavelet-Accelerated Monte Carlo
Computation 2017, 5(4), 44; doi:10.3390/computation5040044 -
Abstract
We present a hierarchical coarse-graining framework for modeling semidilute polymer solutions, based on the wavelet-accelerated Monte Carlo (WAMC) method. This framework forms a hierarchy of resolutions to model polymers at length scales that cannot be reached via atomistic or even standard coarse-grained simulations.
[...] Read more.
We present a hierarchical coarse-graining framework for modeling semidilute polymer solutions, based on the wavelet-accelerated Monte Carlo (WAMC) method. This framework forms a hierarchy of resolutions to model polymers at length scales that cannot be reached via atomistic or even standard coarse-grained simulations. Previously, it was applied to simulations examining the structure of individual polymer chains in solution using up to four levels of coarse-graining (Ismail et al., J. Chem. Phys., 2005, 122, 234901 and Ismail et al., J. Chem. Phys., 2005, 122, 234902), recovering the correct scaling behavior in the coarse-grained representation. In the present work, we extend this method to the study of polymer solutions, deriving the bonded and non-bonded potentials between coarse-grained superatoms from the single chain statistics. A universal scaling function is obtained, which does not require recalculation of the potentials as the scale of the system is changed. To model semi-dilute polymer solutions, we assume the intermolecular potential between the coarse-grained beads to be equal to the non-bonded potential, which is a reasonable approximation in the case of semidilute systems. Thus, a minimal input of microscopic data is required for simulating the systems at the mesoscopic scale. We show that coarse-grained polymer solutions can reproduce results obtained from the more detailed atomistic system without a significant loss of accuracy. Full article
Figures

Figure 1

Open AccessReview
Self-Organizing Map for Characterizing Heterogeneous Nucleotide and Amino Acid Sequence Motifs
Computation 2017, 5(4), 43; doi:10.3390/computation5040043 -
Abstract
A self-organizing map (SOM) is an artificial neural network algorithm that can learn from the training data consisting of objects expressed as vectors and perform non-hierarchical clustering to represent input vectors into discretized clusters, with vectors assigned to the same cluster sharing similar
[...] Read more.
A self-organizing map (SOM) is an artificial neural network algorithm that can learn from the training data consisting of objects expressed as vectors and perform non-hierarchical clustering to represent input vectors into discretized clusters, with vectors assigned to the same cluster sharing similar numeric or alphanumeric features. SOM has been used widely in transcriptomics to identify co-expressed genes as candidates for co-regulated genes. I envision SOM to have great potential in characterizing heterogeneous sequence motifs, and aim to illustrate this potential by a parallel presentation of SOM with a set of numerical vectors and a set of equal-length sequence motifs. While there are numerous biological applications of SOM involving numerical vectors, few studies have used SOM for heterogeneous sequence motif characterization. This paper is intended to encourage (1) researchers to study SOM in this new domain and (2) computer programmers to develop user-friendly motif-characterization SOM tools for biologists. Full article
Open AccessFeature PaperArticle
A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation
Computation 2017, 5(4), 42; doi:10.3390/computation5040042 -
Abstract
We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages
[...] Read more.
We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages for nonlinear systems of equations with diagonally dominant Jacobians, because it is easy to generalize the method to allow for periodic updates of the diagonal of the Jacobian. Systematic tests of the method for atoms show that one can determine the effective Fermi momentum at thousands of points in less than fifteen iterations. Full article
Figures

Figure 1

Open AccessArticle
Modified Equation of Shock Wave Parameters
Computation 2017, 5(3), 41; doi:10.3390/computation5030041 -
Abstract
Among the various blast load equations, the Kingery-Bulmash equation is applicable to both a free-air burst and a surface burst that enables calculations of the parameters of a pressure-time history curve. On the other hand, this equation is quite complicated. This paper proposes
[...] Read more.
Among the various blast load equations, the Kingery-Bulmash equation is applicable to both a free-air burst and a surface burst that enables calculations of the parameters of a pressure-time history curve. On the other hand, this equation is quite complicated. This paper proposes a modified equation that may replace the conventional Kingery-Bulmash equation. The proposed modified equation, which was constructed by performing curve-fitting of this equation, requires a brief calculation process with a simpler equation compared to the original equation. The modified equation is also applicable to both types of bursts and has the same calculable scaled distance range as the conventional equation. The calculation results obtained using the modified equation were similar to the results obtained from the original equation with a less than 1% difference. Full article
Figures

Figure 1

Open AccessArticle
Performance Comparison of Feed-Forward Neural Networks Trained with Different Learning Algorithms for Recommender Systems
Computation 2017, 5(3), 40; doi:10.3390/computation5030040 -
Abstract
Accuracy improvement is among the primary key research focuses in the area of recommender systems. Traditionally, recommender systems work on two sets of entities, Users and Items, to estimate a single rating that represents a user’s acceptance of an item. This technique
[...] Read more.
Accuracy improvement is among the primary key research focuses in the area of recommender systems. Traditionally, recommender systems work on two sets of entities, Users and Items, to estimate a single rating that represents a user’s acceptance of an item. This technique was later extended to multi-criteria recommender systems that use an overall rating from multi-criteria ratings to estimate the degree of acceptance by users for items. The primary concern that is still open to the recommender systems community is to find suitable optimization algorithms that can explore the relationships between multiple ratings to compute an overall rating. One of the approaches for doing this is to assume that the overall rating as an aggregation of multiple criteria ratings. Given this assumption, this paper proposed using feed-forward neural networks to predict the overall rating. Five powerful training algorithms have been tested, and the results of their performance are analyzed and presented in this paper. Full article
Figures

Figure 1

Open AccessReview
Time-Dependent Density-Functional Theory and Excitons in Bulk and Two-Dimensional Semiconductors
Computation 2017, 5(3), 39; doi:10.3390/computation5030039 -
Abstract
In this work, we summarize the recent progress made in constructing time-dependent density-functional theory (TDDFT) exchange-correlation (XC) kernels capable to describe excitonic effects in semiconductors and apply these kernels in two important cases: a “classic” bulk semiconductor, GaAs, with weakly-bound excitons and a
[...] Read more.
In this work, we summarize the recent progress made in constructing time-dependent density-functional theory (TDDFT) exchange-correlation (XC) kernels capable to describe excitonic effects in semiconductors and apply these kernels in two important cases: a “classic” bulk semiconductor, GaAs, with weakly-bound excitons and a novel two-dimensional material, MoS2, with very strongly-bound excitonic states. Namely, after a brief review of the standard many-body semiconductor Bloch and Bethe-Salpether equation (SBE and BSE) and a combined TDDFT+BSE approaches, we proceed with details of the proposed pure TDDFT XC kernels for excitons. We analyze the reasons for successes and failures of these kernels in describing the excitons in bulk GaAs and monolayer MoS2, and conclude with a discussion of possible alternative kernels capable of accurately describing the bound electron-hole states in both bulk and two-dimensional materials. Full article
Figures

Figure 1

Open AccessArticle
CFD-PBM Approach with Different Inlet Locations for the Gas-Liquid Flow in a Laboratory-Scale Bubble Column with Activated Sludge/Water
Computation 2017, 5(3), 38; doi:10.3390/computation5030038 -
Abstract
A novel computational fluid dynamics-population balance model (CFD-PBM) for the simulation of gas mixing in activated sludge (i.e., an opaque non-Newtonian liquid) in a bubble column is developed and described to solve the problem of measuring the hydrodynamic behavior of opaque non-Newtonian liquid-gas
[...] Read more.
A novel computational fluid dynamics-population balance model (CFD-PBM) for the simulation of gas mixing in activated sludge (i.e., an opaque non-Newtonian liquid) in a bubble column is developed and described to solve the problem of measuring the hydrodynamic behavior of opaque non-Newtonian liquid-gas two-phase flow. We study the effects of the inlet position and liquid-phase properties (water/activated sludge) on various characteristics, such as liquid flow field, gas hold-up, liquid dynamic viscosity, and volume-averaged bubble diameter. As the inlet position changed, two symmetric vortices gradually became a single main vortex in the flow field in the bubble column. In the simulations, when water was in the liquid phase, the global gas hold-up was higher than when activated sludge was in the liquid phase in the bubble column, and a flow field that was dynamic with time was observed in the bubble column. Additionally, when activated sludge was used as the liquid phase, no periodic velocity changes were found. When the inlet position was varied, the non-Newtonian liquid phase had different peak values and distributions of (dynamic) liquid viscosity in the bubble column, which were related to the gas hold-up. The high gas hold-up zone corresponded to the low dynamic viscosity zone. Finally, when activated sludge was in the liquid phase, the volume-averaged bubble diameter was much larger than when water was in the liquid phase. Full article
Figures

Figure 1

Open AccessArticle
A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes
Computation 2017, 5(3), 37; doi:10.3390/computation5030037 -
Abstract
The lattice Boltzmann method is an efficient computational fluid dynamics technique that can accurately model a broad range of complex systems. As well as single-phase fluids, it can simulate thermohydrodynamic systems and passive scalar advection. In recent years, it also gained attention as
[...] Read more.
The lattice Boltzmann method is an efficient computational fluid dynamics technique that can accurately model a broad range of complex systems. As well as single-phase fluids, it can simulate thermohydrodynamic systems and passive scalar advection. In recent years, it also gained attention as a means of simulating chemical phenomena, as interest in self-organization processes increased. This paper will present a widely-used and versatile lattice Boltzmann model that can simultaneously incorporate fluid dynamics, heat transfer, buoyancy-driven convection, passive scalar advection, chemical reactions and enthalpy changes. All of these effects interact in a physically accurate framework that is simple to code and readily parallelizable. As well as a complete description of the model equations, several example systems will be presented in order to demonstrate the accuracy and versatility of the method. New simulations, which analyzed the effect of a reversible reaction on the transport properties of a convecting fluid, will also be described in detail. This extra chemical degree of freedom was utilized by the system to augment its net heat flux. The numerical method outlined in this paper can be readily deployed for a vast range of complex flow problems, spanning a variety of scientific disciplines. Full article
Figures

Figure 1

Open AccessArticle
TFF (v.4.1): A Mathematica Notebook for the Calculation of One- and Two-Neutron Stripping and Pick-Up Nuclear Reactions
Computation 2017, 5(3), 36; doi:10.3390/computation5030036 -
Abstract
The program TFF calculates stripping single-particle form factors for one-neutron transfer in prior representation with appropriate perturbative treatment of recoil. Coupled equations are then integrated along a semiclassical trajectory to obtain one- and two-neutron transfer amplitudes and probabilities within first- and second-order perturbation
[...] Read more.
The program TFF calculates stripping single-particle form factors for one-neutron transfer in prior representation with appropriate perturbative treatment of recoil. Coupled equations are then integrated along a semiclassical trajectory to obtain one- and two-neutron transfer amplitudes and probabilities within first- and second-order perturbation theory. Total and differential cross-sections are then calculated by folding with a transmission function (obtained from a phenomenological imaginary absorption potential). The program description, user instructions and examples are discussed. Full article
Figures

Figure 1

Open AccessArticle
Using an Interactive Lattice Boltzmann Solver in Fluid Mechanics Instruction
Computation 2017, 5(3), 35; doi:10.3390/computation5030035 -
Abstract
This article gives an overview of the diverse range of teaching applications that can be realized using an interactive lattice Boltzmann simulation tool in fluid mechanics instruction and outreach. In an inquiry-based learning framework, examples are given of learning scenarios that address instruction
[...] Read more.
This article gives an overview of the diverse range of teaching applications that can be realized using an interactive lattice Boltzmann simulation tool in fluid mechanics instruction and outreach. In an inquiry-based learning framework, examples are given of learning scenarios that address instruction on scientific results, scientific methods or the scientific process at varying levels of student activity, from consuming to applying to researching. Interactive live demonstrations on portable hardware enable new and innovative teaching concepts for fluid mechanics, also for large audiences and in the early stages of the university education. Moreover, selected examples successfully demonstrate that the integration of high-fidelity CFD methods into fluid mechanics teaching facilitates high-quality student research work within reach of the current state of the art in the respective field of research. Full article
Figures

Figure 1

Open AccessArticle
Tensor-Based Semantically-Aware Topic Clustering of Biomedical Documents
Computation 2017, 5(3), 34; doi:10.3390/computation5030034 -
Abstract
Biomedicine is a pillar of the collective, scientific effort of human self-discovery, as well as a major source of humanistic data codified primarily in biomedical documents. Despite their rigid structure, maintaining and updating a considerably-sized collection of such documents is a task of
[...] Read more.
Biomedicine is a pillar of the collective, scientific effort of human self-discovery, as well as a major source of humanistic data codified primarily in biomedical documents. Despite their rigid structure, maintaining and updating a considerably-sized collection of such documents is a task of overwhelming complexity mandating efficient information retrieval for the purpose of the integration of clustering schemes. The latter should work natively with inherently multidimensional data and higher order interdependencies. Additionally, past experience indicates that clustering should be semantically enhanced. Tensor algebra is the key to extending the current term-document model to more dimensions. In this article, an alternative keyword-term-document strategy, based on scientometric observations that keywords typically possess more expressive power than ordinary text terms, whose algorithmic cornerstones are third order tensors and MeSH ontological functions, is proposed. This strategy has been compared against a baseline using two different biomedical datasets, the TREC (Text REtrieval Conference) genomics benchmark and a large custom set of cognitive science articles from PubMed. Full article
Figures

Figure 1

Open AccessArticle
A Discrete Approach to Meshless Lagrangian Solid Modeling
Computation 2017, 5(3), 33; doi:10.3390/computation5030033 -
Abstract
The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles
[...] Read more.
The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles apply stresses expected with Hooke’s law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke’s law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with smoothed particle hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for fluid–solid interactions. Full article
Figures

Figure 1