Article
Mathematics
Jitraj Saha, Andreas Buck
Summary: This article introduces a new numerical scheme for solving multidimensional fragmentation problems, and extends the one-dimensional finite volume scheme to multidimensional cases. The accuracy and efficiency of both schemes are analyzed through several test problems, confirming their validity for solving multidimensional fragmentation problems.
Article
Mathematics, Applied
Saray Busto, Michael Dumbser, Sergey Gavrilyuk, Kseniya Ivanova
Summary: In this paper, a new reformulation of the first order hyperbolic model for unsteady turbulent shallow water flows is proposed, introducing a new evolution variable to ensure non-negativity of the trace of the discrete Reynolds stress tensor. Two different but related families of numerical methods are introduced, including a high order path-conservative ADER discontinuous Galerkin finite element method with subcell finite volume limiter.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Hideki Yanaoka
Summary: In this study, a conservative finite difference method is constructed for incompressible magnetohydrodynamic (MHD) flows considering the induced magnetic field. The difference in energy conservation properties among three methods of calculating the Lorentz force is compared. The results show that using compact interpolation to calculate the Lorentz force can better preserve total energy conservation and accurately predict energy conversion.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Kaibo Hu, Young-Ju Lee, Jinchao Xu
Summary: The study introduces finite element methods for the incompressible magnetohydrodynamics (MHD) system that accurately preserve the magnetic and cross helicity, the energy law and the magnetic Gauss law at the discrete level. Numerical tests are presented to demonstrate the algorithm's performance.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Elena Gaburro, Michael Dumbser
Summary: This work introduces the ADER P-N P-M schemes for high-order accuracy in solving hyperbolic partial differential equations, and presents an effective subcell finite volume limiting strategy to address discontinuities while maintaining high resolution.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Hongyang Luo, John G. Lyon, Binzheng Zhang
Summary: In many astrophysical plasmas, anisotropic temperature is observed due to insufficient Coulomb collision. To describe such plasma system, anisotropic pressure MHD models are needed. A robust Gas-Kinetic flux scheme is developed to numerically solve the anisotropic MHD equation. The scheme performs well for both linear wave and non-linear MHD problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
A. Mignone, L. Del Zanna
Summary: The research focuses on comparing and extending existing upwind constrained transport methods for maintaining robustness and accuracy in MHD simulations, while proposing a new flux formula applicable to the induction equation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Haruhisa Iijima
Summary: In this paper, an energy-consistent finite difference formulation for the compressible hydrodynamic and magnetohydrodynamic equations is introduced. Conservation properties of internal, kinetic, and magnetic energy equations are satisfied at the discrete level without explicitly solving the total energy equation through nonlinear filtering schemes. The proposed schemes successfully handle the most stringent problems in extremely high Mach number and low beta conditions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Jonas P. Berberich, Praveen Chandrashekar, Christian Klingenberg
Summary: The study introduces a general framework for constructing well-balanced finite volume methods for hyperbolic balance laws. The proposed method can be applied to follow any solution of any system of hyperbolic balance laws in multiple spatial dimensions. By modifying the standard finite volume approach, the well-balancing property is achieved and maintained even with high order accuracy.
COMPUTERS & FLUIDS
(2021)
Article
Computer Science, Interdisciplinary Applications
G. Saez-Mischlich, J. Sierra-Ausin, G. Grondin, J. Gressier
Summary: This paper studies the performance of high-order finite-volume schemes based on polynomial least-squares methods in different meshes and compares them with polynomial reconstructions compatible with structured meshes. The results show that high-order least-squares finite volume schemes yield stable and robust results in different uniform and non-uniform unstructured meshes, but their performance degrades in simulations with low mesh resolution. On the other hand, schemes catered to structured meshes lack stability and robustness in general and cannot be directly extended to unstructured meshes. Weighted least-squares methods can significantly improve the results of LSQ schemes in under-resolved simulations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Panagiotis Tsoutsanis, Ebenezer Mayowa Adebayo, Adrian Carriba Merino, Agustin Perez Arjona, Martin Skote
Summary: This paper extends the application of high-order finite-volume central-weighted essentially non-oscillatory (CWENO) schemes to multicomponent flows using the interface capturing paradigm, achieving high-order accurate and oscillation free solutions. The schemes are compact and perform well, but have limitations within the present interface-capturing implementation.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Yongsheng Chen, Wei Guo, Xinghui Zhong
Summary: In this work, a novel machine learning-assisted approach to accelerate the conventional SL finite volume (FV) schemes is proposed. The method incorporates specific inductive biases in the neural network to learn the SL discretization from data, avoiding the expensive tracking of upstream cells. Numerical tests demonstrate the effectiveness and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Ernesto Pimentel-Garcia, Manuel J. Castro, Christophe Chalons, Tomas Morales de Luna, Carlos Pares
Summary: This paper presents a new strategy for the numerical approximation of discontinuous solutions in non-conservative hyperbolic systems, with a second-order extension. The method captures isolated shocks accurately and maintains the well-balanced property. Numerical tests are conducted to validate the effectiveness of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Gengen Zhang
Summary: Two conservative and linearly-implicit difference schemes are proposed for solving the nonlinear fourth-order wave equation with periodic boundary conditions. These schemes, based on two different compact finite difference discretizations, are shown to be fourth-order accurate in space and second-order accurate in time. Numerical experiments confirm the theoretical results, including the discrete energy conservation properties of the developed schemes.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Qian-Min Huang, Yu-Xin Ren, Qian Wang
Summary: In this paper, a high order finite volume scheme for solving the non-conservative convection equations on unstructured grids is proposed. To address numerical instability and singularity issues, the integral form of the equations is solved using a convective reconstruction technique and artificial viscosity term. Numerical results demonstrate that the proposed method achieves high order accuracy and robustness.
JOURNAL OF SCIENTIFIC COMPUTING
(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)