Search Results (203)

To address the need for high-efficiency vibration isolation in marine rotary pump units, this paper proposes a coupled isolation system that integrates vibration isolators and flexible connectors, and systematically investigates its vibration suppression performance. By combining experimental parameterized modeling with full-scale test platform validation, an efficient analytical framework capable of accurately predicting the system’s broadband vibration isolation performance has been established. This framework provides a reference for engineering design that balances model reliability and practical applicability. The study first obtained the transfer complex stiffness of the isolators through mechanical impedance experiments and, combined with the stiffness parameters of the flexible connectors measured by an MTS (Mechanical Testing & Simulation) testing machine, established a nonlinear spring-damper equivalent model for the isolators and flexible connectors. A three-dimensional finite element model of the rotary pump unit coupled isolation system was developed using the explicit dynamics method, and the vibration transmission characteristics of the coupled isolation system under complex excitation from the rotary pump were analyzed using the vibration acceleration level difference between the “machine foot” and “foundation” as the evaluation index. To verify the reliability of the model, a full-scale rotary pump unit isolation test platform was constructed, and multi-condition vibration tests were conducted. The results show that the finite element model of the coupled isolation system can effectively predict the vibration response, with the overall vibration level error between numerical calculations and experiments within ±3 dB. Under various operating conditions involving changes in rotational speed and water pressure, the system demonstrates good broadband isolation performance, with the maximum vibration acceleration level difference reaching 29.32 dB. The flexible connectors further suppress lateral vibration transmission from the pump unit to external pipelines, working in synergy with the isolators to achieve multi-directional vibration isolation. This study provides design references with both modeling reliability and engineering applicability for vibration and noise reduction in marine pump units. Full article

Multiphase flow in porous media is ubiquitous in physical processes, yet modeling it consistently remains difficult, and sometimes it can be coupled with solid-phase decomposition and phase change, such as in hydrate dissociation or internal erosion processes. Recent code comparison studies have highlighted this difficulty, revealing clear inconsistencies in numerical results across different research groups for the same benchmark problem. This paper presents a new, reliable benchmark test and a hybrid explicit-implicit finite element method adaptable to various scenarios. In our mathematical framework, the solid decomposition is described by a rate equation for porosity that depends on the fluid pressure, and the phase change is modeled via mass source terms. The hybrid explicit-implicit finite element method features a novel three-stage updating strategy, which incorporates an artificial diffusion term and carefully selects the transport equation for the final saturation update. Validation results demonstrate that our proposed method achieves substantial agreement with those of the fully implicit finite volume method, confirming its reliability. Furthermore, our analysis confirms that the saturation update must use the transport equation of the incompressible fluid phase, and that the artificial diffusion term is critical for capturing physically correct saturation profiles, even when advection is not dominant. Overall, this work provides a consistent and effective tool for simulating complex multiphase flow scenarios and serves as a valuable complement to future benchmark studies. Full article

In this work, a high-order meshless framework is developed for the numerical resolution of the temporal–fractional Black–Scholes equation arising in option pricing with long-memory effects. The spatial discretization is carried out with a local radial basis function produced finite difference (RBF–FD) method on seven-node stencils. Analytical differentiation weights are constructed by employing closed-form second integrations of a variant of the inverse multiquadric kernel, which yields sparse differentiation matrices. Explicit formulas are derived for both first- and second-order operators, and a detailed truncation error analysis confirms sixth-order convergence in space. Numerical experiments for European options discuss better accuracy per spatial node than standard finite difference schemes. Full article

Guided by principles of symmetry to achieve a proper balance among model consistency, accuracy, and complexity, this paper proposes a new approach for identifying the unknown parameters of nonlinear one-degree-of-freedom mechanical systems using nonlinear regression methods. To this end, the steps followed in this study can be summarized as follows. Firstly, given a proper set of input time histories and a virtual model with all parameters known, the dynamic response of the mechanical system of interest, used as output data, is evaluated using a numerical integration scheme, such as the classical explicit fixed-step fourth-order Runge–Kutta method. Secondly, the numerical values of the unknown parameters are estimated using the Levenberg–Marquardt nonlinear regression algorithm based on these inputs and outputs. To demonstrate the effectiveness of the proposed approach through numerical experiments, two benchmark problems are considered, namely a mass-spring-damper system and a simple pendulum-damper system. In both mechanical systems, viscous damping is included at the kinematic joints, whereas dry friction between the bodies and the ground is accounted for and modeled using the Coulomb friction force model. While the source of nonlinearity is the frictional interaction alone in the first benchmark problem, the finite rotation of the pendulum introduces geometric nonlinearity, in addition to the frictional interaction, in the second benchmark problem. To ensure symmetry in explaining model behavior and the interpretability of numerical results, the analysis presented in this paper utilizes five different input functions to validate the proposed method, representing the initial phase of ongoing research aimed at applying this identification procedure to more complex mechanical systems, such as multibody and robotic systems. The numerical results from this research demonstrate that the proposed approach effectively identifies the unknown parameters in both benchmark problems, even in the presence of nonlinear, time-varying external input actions. Full article

This study presents a theoretical framework for modeling sorption and release kinetics of substances in polymeric materials with planar, cylindrical, and spherical geometries. Fick’s second law was expressed in dimensionless variables and solved numerically using a finite-difference approach to generate universal profiles for mass transfer. These profiles were fitted with double-exponential equations, yielding explicit expressions that allow for straightforward estimation of diffusion coefficients from experimental data. The method was validated using literature data for films, fibers, and microspheres, showing excellent agreement with reported values. Unlike classical analytical solutions, which are limited to planar systems under ideal conditions, the proposed approach is applicable to diverse geometries commonly employed in packaging, biomedical devices, controlled-release formulations, and environmental technologies. Full article

The FitzHugh–Nagumo (FHN) equation in one dimension is solved in this paper using an improved physics-informed neural network (PINN) approach. Examining test problems with known analytical solutions and the explicit finite difference method (EFDM) allowed for the demonstration of the PINN’s effectiveness. Our study presents an improved PINN formulation tailored to the FitzHugh–Nagumo reaction–diffusion system. The proposed framework is efficiently designed, validated, and systematically optimized, demonstrating that a careful balance among model complexity, collocation density, and training strategy enables high accuracy within limited computational time. Despite the very strong agreement that both methods provide, we have demonstrated that the PINN results exhibit a closer agreement with the analytical solutions for Test Problem 1, whereas the EFDM yielded more accurate results for Test Problem 2. This study is crucial for evaluating the PINN’s performance in solving the FHN equation and its application to nonlinear processes like pulse propagation in optical fibers, drug delivery, neural behavior, geophysical fluid dynamics, and long-wave propagation in oceans, highlighting the potential of PINNs for complex systems. Numerical models for this class of nonlinear partial differential equations (PDEs) may be developed by existing and future model creators of a wide range of various nonlinear physical processes in the physical and engineering sectors using the concepts of the solution methods employed in this study. Full article

For extracting oil and gas from low-permeability reservoirs, pulse hydraulic fracturing offers superior performance over conventional hydraulic fracturing. Pulse hydraulic fracturing employs variable-rate injection to create pressure waves, which significantly increases the recovery rate. However, current pulse hydraulic fracturing research primarily focuses on the wellbore. The theory describing how pressure waves propagate and attenuate within fractures is still immature, potentially hindering the achievement of optimal fracture propagation and diversion. A two-dimensional pressure-wave equation incorporating both steady and unsteady friction was established and numerically solved using a high-accuracy explicit compact finite-difference method and was validated. The propagation process and pressurization phenomenon of pressure waves were analyzed, and the effects of treatment frequency, amplitude, and waveform, as well as steady and unsteady friction coefficients, on the attenuation characteristics of pressure waves within fractures were analyzed. The model’s validity is based on the pad fluid stage of hydraulic fracturing, informing the rational selection of treatment parameters in engineering practice, thereby improving fracturing performance and having practical significance for enhancing the development efficiency of low-permeability reservoirs. Full article

A variety of methods that provide approximate piecewise- analytical solutions to initial-value problems governed by scalar, nonlinear, first-order, ordinary differential equations is presented. The methods are based on fixing the independent variable in the right-hand side of these equations and approximating the resulting term by either its first- or second-order Taylor series expansion. It is shown that the second-order Taylor series approximation results in Riccati equations with constant coefficients, whereas the first-order one results in first-order, linear, ordinary differential equations. Both approximations are shown to result in explicit finite difference equations that are unconditionally linearly stable, and their local truncation errors are determined. It is shown that, for three of the nonlinear, first-order, ordinary differential equations studied in this paper that are characterized by growing or decaying solutions, as well as by solutions that first grow and then decrease, a second-order Taylor series expansion of the right-hand side of the differential equation evaluated at each interval’s midpoint results in the most accurate method; however, the accuracy of this method degrades substantially for problems that exhibit either blowup in finite time or quadratic approximations characterized by a negative radicand. It is also shown that methods based on either first- or second-order Taylor series expansion of the right-hand side of the differential equation evaluated at either the left or the right points of each interval have similar accuracy, except for one of the examples that exhibits blowup in finite time. It is also shown that both the linear and the quadratic approximation methods that use the midpoint for the independent variable in each interval exhibits the same trends as and have errors comparable to the second-order trapezoidal technique. Full article

This paper investigates D-finite discrete generating series and their sections. The concept of D-finiteness is extended to multidimensional discrete generating series and its equivalence to p-recursive sequences is rigorously established. It is further shown that sections of the D-finite series preserve D-finiteness, and that their generating functions satisfy systems of linear difference equations with polynomial coefficients. In the two-dimensional case, explicit difference relations are derived that connect section values with boundary data, while in higher dimensions general constructive methods are developed for obtaining such relations, including cases with variable coefficients. Several worked examples illustrate how the theory applies to solving difference equations and analyzing multidimensional recurrent sequences. The results provide a unified framework linking generating functions and recurrence relations, with applications in combinatorics, number theory, symbolic summation, and the theory of discrete recursive filters in signal processing. Full article

This article presents an optimization of the explicit Euler method for a heat conduction model. The starting point of the paper was the analysis of the limitations of the explicit Euler scheme and the classical CFL condition in the transient domain, which pointed to the oscillation occurring in the intermediate states. To eliminate this phenomenon, we introduced the No-Sway Threshold given for the Fourier number (K), stricter than the CFL, which guarantees the monotonic approximation of the temperature–time evolution. Thereafter, by means of the identical inequalities derived based on the Method of Equating Coefficients, we determined the optimal values of $\Delta t$ and $\Delta x$. Finally, for the construction of the variable grid spacing (M2), we applied the equation expressing the R of the identical inequality system and accordingly specified the thickness of the material elements ($\Delta \xi$). As a proof-of-concept, we demonstrate the procedure on an application case with major simplifications: during an emergency shutdown of the Flexblue® SMR, the temperature of the air inside the tank instantly becomes 200 °C, while the initial temperatures of the water and the steel are 24 °C. For a 50.003 mm × 50.003 mm surface patch of the tank, we keep the leftmost and rightmost material elements of the uniform-grid (M1) and variable-grid (M2) single-line models at constant temperature; we scale the results up to the total external surface (6714.39 m²). In the M2 case, a larger portion of the heat power taken up from the air is expended on heating the metal, while the rise in the heat power delivered to the seawater is more moderate. At the 3000th min, the steel-wall temperature in M1 falls between 26.229 °C and 25.835 °C, whereas in M2 the temperature gradient varies between 34.648 °C and 30.041 °C, which confirms the advantage of the combination of variable grid spacing and the No-Sway Threshold. Full article

In this paper, we develop the explicit finite difference method (FDM) to solve an ill-posed Cauchy problem for the 3D acoustic wave equation in a time domain with the data on a part of the boundary given (continuation problem) in a cube. FDM is one of the numerical methods used to compute the solutions of hyperbolic partial differential equations (PDEs) by discretizing the given domain into a finite number of regions and a consequent reduction in given PDEs into a system of linear algebraic equations (SLAE). We present a theory, and through Matlab Version: 9.14.0.2286388 (R2023a), we find an efficient solution of a dense system of equations by implementing the numerical solution of this approach using several iterative techniques. We extend the formulation of the Jacobi, Gauss–Seidel, and successive over-relaxation (SOR) iterative methods in solving the linear system for computational efficiency and for the properties of the convergence of the proposed method. Numerical experiments are conducted, and we compare the analytical solution and numerical solution for different time phenomena. Full article

The initial part of this study fills a notable research gap by investigating the substantial impact of numerical diffusion errors from different schemes on sloshing tank models. Multiple numerical models were developed: first- and higher-order upwind schemes equipped with precise wall treatment using ghost nodes, MacCormack and central methods that are explicit second-order finite difference methods, and Preissmann and staggered methods employed in full-implicit and semi-implicit modes. Furthermore, the separation of variables technique was proposed for simulating sloshing tanks and deriving an analytical equation for the tank’s natural period. An analytical solution to the perturbation was employed to examine the numerical diffusion of the schemes. Subsequently, two sloshing tests, resonant and near-resonant excitations, were employed to determine the numerical diffusion and calibrate the physical diffusion coefficients, respectively. Finally, an efficient and accurate numerical scheme was applied to a linear shallow water model including physical diffusion and coupled with a single degree of freedom (SDOF), to simulate tuned liquid dampers (TLDs). It shows that the efficiency of TLD is associated with a compact domain around resonance excitation. Contrary to SDOF alone, when SDOF interacts with TLD the impact of structural damping on reducing the response is minimal in resonance excitation. Full article

The efficiency of various numerical methods for solving Huxley’s equation—which includes a diffusion term and a nonlinear reaction term—is investigated. Conventional explicit finite difference algorithms often suffer from severe stability limitations and can yield unphysical concentration values. In this study, we collect a range of stable, explicit time integration methods of first to fourth order, originally developed for the diffusion equation, and design treatments of the nonlinear term which ensure that the solution remains within the physically meaningful unit interval. This property, called dynamical consistency, is analytically proven and implies unconditional stability. In addition to this, the most effective ones are identified from the large number of constructed method combinations. We conduct systematic tests in one and two spatial dimensions, also evaluating computational efficiency in terms of CPU time. Our results show that higher-order schemes are not always the most efficient: in certain parameter regimes, second-order methods can outperform their higher-order counterparts. Full article

We develop a high-order compact numerical scheme for solving a nonlinear Black–Scholes equation arising in option pricing under transaction costs. By leveraging a Hermite-enhanced Radial Basis Function-Finite Difference (RBF-HFD) method with three-point stencils, we achieve fourth-order spatial accuracy. The fully nonlinear PDE, driven by Gamma-dependent volatility models, is discretized via RBF-HFD in space and integrated using an explicit sixth-order Runge–Kutta scheme. Numerical results confirm the proposed method’s accuracy, stability, and its capability to capture sharp gradient behavior near strike prices. Full article

This paper investigates the inverse reconstruction of temperature fields under both steady-state and transient heat conduction scenarios. The central contribution lies in the structured development and validation of the Gappy Clustering-based Proper Orthogonal Decomposition (Gappy C-POD) method—an approach that, despite its conceptual origin alongside the clustering-based dimensionality reduction method guided by POD structures (C-POD), had previously lacked an explicit algorithmic framework or experimental validation. To this end, the study constructs a comprehensive solution framework that integrates sparse sensor layout optimization with data-driven field reconstruction techniques. Numerical models incorporating multiple internal heat sources and heterogeneous boundary conditions are solved using the finite difference method. Multiple sensor layout strategies—including random selection, S-OPT, the Correlation Coefficient Filtering Method (CCFM), and uniform sampling—are evaluated in conjunction with database generation techniques such as Latin Hypercube sampling, Sobol sequences, and maximum–minimum distance sampling. The experimental results demonstrate that both Gappy POD and Gappy C-POD exhibit strong robustness in low-modal scenarios (1–5 modes), with Gappy C-POD—when combined with the CCFM and maximum distance sampling—achieving the best reconstruction stability. In contrast, while POD-MLP and POD-RBF perform well at higher modal numbers (>10), they show increased sensitivity to sensor configuration and sample size. This research not only introduces the first complete implementation of the Gappy C-POD methodology but also provides a systematic evaluation of reconstruction performance across diverse sensor placement strategies and reconstruction algorithms. The results offer novel methodological insights into the integration of data-driven modeling and sensor network design for solving inverse temperature field problems in complex thermal environments. Full article