Article
Computer Science, Interdisciplinary Applications
Fei Fei
Summary: In this paper, a new time-relaxed Monte Carlo (TRMC) method is proposed for the inhomogeneous Boltzmann equation. Compared to the standard TRMC scheme, the proposed method divides the collision operator by a micro-macro decomposition while performing the same convection operator. The new TRMC method demonstrates the same accuracy as the standard TRMC scheme in the kinetic limit, however, preserves Navier-Stokes asymptotics and the second-order accuracy in the fluid limit. Several numerical cases of inhomogeneous flows are calculated and compared with direct simulation Monte Carlo (DSMC) or Navier-Stokes solutions, showing that the new TRMC scheme is more accurate and efficient.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Chemistry, Physical
Ziqi Guo, Prabudhya Roy Chowdhury, Zherui Han, Yixuan Sun, Dudong Feng, Guang Lin, Xiulin Ruan
Summary: Researchers have developed a machine learning approach that accurately predicts phonon scattering rates and thermal conductivity with experimental and first principles accuracy. This method overcomes the complexity and high computational cost associated with phonon scattering calculations, and enables large-scale thermal transport informatics.
NPJ COMPUTATIONAL MATERIALS
(2023)
Article
Thermodynamics
Chuang Zhang, Songze Chen, Zhaoli Guo, Lei Wu
Summary: This paper introduces a fast synthetic iterative scheme to accelerate the convergence of the implicit discrete ordinate method for non-equilibrium heat transfer problems. The innovative scheme effectively addresses the issue of slow convergence from the diffusive to ballistic regimes.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2021)
Article
Mathematics, Applied
Yupeng Ren, Yulong Xing, Dean Wang, Jianxian Qiu
Summary: In this paper, the combination of HWENO scheme and FSM method is proposed for solving the steady-state S-N transport equation in the finite volume framework. The asymptotic preserving property of the high order finite volume HWENO method is demonstrated, and a hybrid strategy is introduced to compute the nonlinear weights in the HWENO reconstruction for computational efficiency improvement.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Physics, Mathematical
Jia Liu, Lei Wu
Summary: In this study, we propose a general synthetic iterative scheme (GSIS) to solve the phonon Boltzmann equation, which has fast convergence and asymptotic-preserving properties. We find that the heating frequency affects the heat conduction in different transport regimes.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Min Tang, Li Wang, Xiaojiang Zhang
Summary: The translation discusses an asymptotic preserving scheme for the gray radiative transfer equation, introducing an auxiliary variable to solve an implicit nonlinear system and using a three-stage update. The method preserves accurate simulation results in both the nonlinear diffusion limit and the free streaming limit.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Jingwei Hu, Xiaodong Huang, Jie Shen, Haizhao Yang
Summary: In this paper, a Petrov-Galerkin spectral method for the Boltzmann equation in unbounded domain is introduced. The method utilizes carefully chosen mapped Chebyshev functions as basis functions to achieve desired convergence and conservation properties. The proposed method is shown to have superior accuracy compared to the Fourier spectral method through a series of two-dimensional and three-dimensional examples.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Jinxue Fu, Weiming Li, Peng Song, Yanli Wang
Summary: In this paper, an asymptotic preserving method is presented for solving the radiative transfer equations using the P-N method. The order analysis of expansion coefficients is conducted to propose an implicit and explicit numerical scheme for the P-N system. The efficiency of this scheme is validated through numerical examples in both optically thick and thin regions.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Interdisciplinary Applications
Yanan Li, Yibin Xu, Yanqin Liu, Yanfeng Shen
Summary: In this work, a fast ? scheme combined with the Legendre spectral method was developed for solving a fractional Klein-Gordon equation. The numerical scheme employed the Legendre spectral method in the spatial direction and a ? scheme of order O(t(2)) with a fast algorithm in the temporal direction. The fast algorithm reduced the computational cost from O(t(2)) to O(M log M), where M is the number of time levels. Correction terms could be used to improve the convergence rate, especially when the solutions have weak regularity. The scheme was proven to be unconditionally stable and an error estimate was obtained. Numerical experiments demonstrated the accuracy and efficiency of the scheme.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Interdisciplinary Applications
Tianbai Xiao, Martin Frank
Summary: The paper introduces a new stochastic kinetic scheme that includes uncertainties for studying multi-scale non-equilibrium gas dynamics, with numerical experiments validating its effectiveness. New physical observations such as wave-propagation patterns of uncertainties in different flow regimes were discovered through this scheme.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
L. O. R. E. N. Z. O. PARESCHI, T. H. O. M. A. S. REY
Summary: In this paper, a novel Fourier-Galerkin spectral method is introduced to approximate collisional kinetic equations in kinetic theory. The method improves the classical spectral method by conserving the moments of the approximated distribution, while still maintaining spectral accuracy and the possibility of using fast algorithms. The method is derived using a constrained best approximation in the space of trigonometric polynomials and can be applied to a wide range of problems. The spectral consistency and stability of the resulting Fourier-Galerkin approximation scheme are proven through numerical experiments.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2022)
Article
Computer Science, Interdisciplinary Applications
Luis Almeida, Benoit Perthame, Xinran Ruan
Summary: The study introduces an asymptotic preserving (A-P) scheme for a population model structured by age and a phenotypical trait, demonstrating the accuracy and numerical resolution capability of the scheme. The scheme exhibits the A-P property and is applicable even in cases with mutations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Ruo Li, Yixiao Lu, Yanli Wang, Haoxuan Xu
Summary: This paper presents a numerical scheme based on Hermite spectral method for solving the multi-species Boltzmann equation. By choosing proper expansion centers and collision models, a balance between computational cost and accuracy is achieved, and high-dimensional problems can be handled effectively.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Jia Liu, Chuang Zhang, Haizhuan Yuan, Wei Su, Lei Wu
Summary: This study proposes a general synthetic iterative scheme (GSIS) to solve the heat conduction problem in semiconductor materials when the classical Fourier's law is no longer valid. Compared to the conventional iterative scheme, GSIS achieves faster convergence and higher computational efficiency, especially in the diffusive and hydrodynamic regimes with small Knudsen numbers.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Lorenzo Pareschi, Thomas Rey
Summary: The article introduces the effectiveness of using spectral methods to approximate the Boltzmann collision operator, and proposes an equilibrium-preserving spectral method to overcome the wrong long time behavior. Through perturbation arguments, the stability, convergence, and spectrally accurate long time behavior of the method are proven.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)