arXiv subjects

Minsheng Huang

Publications and source records attributed to Minsheng Huang.

7 recordsLinked to original sources

arXiv2026

ADI schemes for heat equations with irregular boundaries and interfaces in 3D with applications

In this paper, efficient alternating direction implicit (ADI) schemes are proposed to solve three-dimensional heat equations with irregular boundaries and interfaces. Starting from the well-known Douglas-Gunn ADI scheme, a modified ADI scheme is constructed to mitigate the issue of accuracy loss in solving problems with time-dependent boundary conditions. The unconditional stability of the new ADI scheme is also rigorously proven with the Fourier analysis. Then, by combining the ADI schemes with a 1D kernel-free boundary integral (KFBI) method, KFBI-ADI schemes are developed to solve the heat equation with irregular boundaries. In 1D sub-problems of the KFBI-ADI schemes, the KFBI discretization takes advantage of the Cartesian grid and preserves the structure of the coefficient matrix so that the fast Thomas algorithm can be applied to solve the linear system efficiently. Second-order accuracy and unconditional stability of the KFBI-ADI schemes are verified through several numerical tests for both the heat equation and a reaction-diffusion equation. For the Stefan problem, which is a free boundary problem of the heat equation, a level set method is incorporated into the ADI method to capture the time-dependent interface. Numerical examples for simulating 3D dendritic solidification phenomenons are also presented.

math.NA↗

arXiv2025

A low-dissipation reconstruction scheme for compressible single- and multi-phase flows based on artificial neural networks

Solving compressible flows containing both smooth and discontinuous flow structures remains a significant challenge for finite volume methods. Godunov-type finite volume methods are commonly used for numerical simulations of compressible flows. One of the key factors in obtaining high-quality solutions is high-fidelity spatial reconstruction. In this work, we introduce a new paradigm for constructing high-resolution hybrid reconstruction schemes for compressible flows. This approach generates training data based on BVD schemes for supervised learning and employs ANN to create an indicator that pre-selects the most suitable reconstruction scheme for each cell, achieving the lowest global numerical dissipation. The numerical schemes under this paradigm are more computationally efficient than similar schemes within the BVD framework, as each cell only requires constructing a single interpolation function. Following this paradigm, a novel low-dissipation reconstruction scheme based on the MUSCL-THINC-BVD scheme, named the deepMTBVD scheme, is proposed for compressible single- and multi-phase flows. The performance of the proposed scheme has been extensively verified through benchmark tests of single- and multi-phase compressible flows, where discontinuous and vortical flow structures, like shock waves, contact discontinuities, and material interfaces, as well as vortices and shear instabilities of different scales, coexist simultaneously. Numerical results indicate that the new deepMTBVD scheme performs as well as the original MUSCL-THINC-BVD scheme for numerical simulations of compressible flows while reducing computational time by up to 40%.

physics.flu-dyn↗

arXiv2024

An Efficient Monte Carlo Simulation for Radiation Transport Based on Global Optimal Reference Field

The reference field method, known as the difference formulation, is a key variance reduction technique for Monte Carlo simulations of thermal radiation transport problems. When the material temperature is relatively high and the spatial temperature gradient is moderate, this method demonstrates significant advantages in reducing variance compared to classical Monte Carlo methods. However, in problems with larger temperature gradients, this method has not only been found ineffective at reducing statistical noise, but in some cases, it even increases noise compared to classical Monte Carlo methods. The global optimal reference field method, a recently proposed variance reduction technique, effectively reduces the average energy weight of Monte Carlo particles, thereby decreasing variance. Its effectiveness has been validated both theoretically and numerically, demonstrating a significant reduction in statistical errors for problems with large temperature gradients. In our previous work, instead of computing the exact global optimal reference field, we developed an approximate, physically motivated method to find a relatively better reference field using a selection scheme. In this work, we reformulate the problem of determining the global optimal reference field as a linear programming problem and solve it exactly. To further enhance computational efficiency, we use the MindOpt solver, which leverages graph neural network methods. Numerical experiments demonstrate that the MindOpt solver not only solves linear programming problems accurately but also significantly outperforms the Simplex and interior-point methods in terms of computational efficiency. The global optimal reference field method combined with the MindOpt solver not only improves computational efficiency but also substantially reduces statistical errors.

physics.comp-ph↗

arXiv2024

A Robust and Efficient Multi-physics Numerical System for Intensive Blast Wave Propagation in Complex Environments

We establish a high-resolution, high-performance, and high-confidence compressible multiphysics system in a Cartesian grid with irregular boundary topologies to simulate intensive blast waves propagating in large-scale and extremely complex environments. The multiphysics system is modeled by a multi-component model solved using a generalized Godunov method and a classical material point method in a combination of Lagrangian particles and a rigid material model. An artificial neural network equation of state (EOS) is proposed based on experimental data to simulate the intensive explosion products and real gas under extreme pressure and temperature. To improve computational accuracy and efficiency, a deepMTBVD reconstruction scheme of our previous work is extended to the multiphysics system. With the aid of high-performance parallel computation, several large-scale blast wave applications, such as blast wave propagating in a local and entire urban city, are simulated in a reasonable time period, which can validate numerical schemes and lead to more practical engineering applications.

physics.comp-ph↗

arXiv2024

A GPU-accelerated Cartesian grid method is proposed for solving the heat, wave, and Schrodinger equations on irregular domains

This paper introduces a second-order method for solving general elliptic partial differential equations (PDEs) on irregular domains using GPU acceleration, based on Ying's kernel-free boundary integral (KFBI) method. The method addresses limitations imposed by CFL conditions in explicit schemes and accuracy issues in fully implicit schemes for the Laplacian operator. To overcome these challenges, the paper employs a series of second-order time discrete schemes and splits the Laplacian operator into explicit and implicit components. Specifically, the Crank-Nicolson method discretizes the heat equation in the temporal dimension, while the implicit scheme is used for the wave equation. The Schrodinger equation is treated using the Strang splitting method. By discretizing the temporal dimension implicitly, the heat, wave, and Schrodinger equations are transformed into a sequence of elliptic equations. The Laplacian operator on the right-hand side of the elliptic equation is obtained from the numerical scheme rather than being discretized and corrected by the five-point difference method. A Cartesian grid-based KFBI method is employed to solve the resulting elliptic equations. GPU acceleration, achieved through a parallel Cartesian grid solver, enhances the computational efficiency by exploiting high degrees of parallelism. Numerical results demonstrate that the proposed method achieves second-order accuracy for the heat, wave, and Schrodinger equations. Furthermore, the GPU-accelerated solvers for the three types of time-dependent equations exhibit a speedup of 30 times compared to CPU-based solvers.

math.NA↗

arXiv2024

A GPU-accelerated Cartesian grid method for PDEs on irregular domain

The kernel-free boundary integral (KFBI) method has successfully solved partial differential equations (PDEs) on irregular domains. Diverging from traditional boundary integral methods, the computation of boundary integrals in KFBI is executed through the resolution of equivalent simple interface problems on Cartesian grids, utilizing fast algorithms. While existing implementations of KFBI methods predominantly utilize CPU platforms, GPU architecture's superior computational capabilities and extensive memory bandwidth offer an efficient resolution to computational bottlenecks. This paper delineates the algorithms adapted for both single-GPU and multiple-GPU applications. On a single GPU, assigning individual threads can control correction, interpolation, and jump calculations. The algorithm is expanded to multiple GPUs to enhance the processing of larger-scale problems. The arrowhead decomposition method is employed in multiple-GPU settings, ensuring optimal computational efficiency and load balancing. Numerical examples show that the proposed algorithm is second-order accurate and efficient. Single-GPU solver speeds 50-200 times than traditional CPU while the eight GPUs distributed solver yields up to 60% parallel efficiency.

math.NA↗

arXiv2024

Physics-informed Data-driven Cavitation Model for a Specific MG EOS

We present a novel one-fluid cavitation model of a specific Mie-Grüneisen equation of state(EOS), named polynomial EOS, based on an artificial neural network. Not only the physics-informed equation but also the experimental data are embedded into the proposed model by an optimization problem. The physics-informed data-driven model provides the concerned pressure within the cavitation region, where the density tends to zero when the pressure falls below the saturated pressure. The present model is then applied to computing the challenging compressible multi-phase flow simulation, such as nuclear and underwater explosions. Numerical simulations show that our model in application agrees well with the corresponding experimental data, ranging from one dimension to three dimensions with the $h-$adaptive mesh refinement algorithm and load balance techniques in the structured and unstructured grid.

physics.flu-dyn↗