4.6 Article

A High-Order Residual-Based Viscosity Finite Element Method for the Ideal MHD Equations

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

Residual Viscosity Stabilized RBF-FD Methods for Solving Nonlinear Conservation Laws

Igor Tominec et al.

Summary: This paper presents a radial basis function generated finite difference method for solving nonlinear conservation laws, addressing the issue of numerical instabilities through the introduction of a residual-based artificial viscosity stabilization framework. Computational tests confirm the reliability and accuracy of the proposed stabilized methods in solving both scalar conservation laws and conservation law systems.

JOURNAL OF SCIENTIFIC COMPUTING (2023)

Article Computer Science, Interdisciplinary Applications

A residual-based artificial viscosity finite difference method for scalar conservation laws

Vidar Stiernstrom et al.

Summary: This paper presents an accurate, stable, and robust shock-capturing finite difference method for solving scalar non-linear conservation laws. The method utilizes high-order accurate upwind finite difference operators, residual-based error estimators for shock detection, and first-order viscosity in regions with strong discontinuities. The method also includes additional damping of spurious oscillations from high-order dissipation, showing stability for skew-symmetric discretizations. Accuracy and robustness are demonstrated through solving benchmark problems with convex and non-convex fluxes in 2D.

JOURNAL OF COMPUTATIONAL PHYSICS (2021)

Article Computer Science, Interdisciplinary Applications

Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations

Dmitri Kuzmin et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2020)

Article Mathematics, Applied

Skew-Symmetric Splitting for Multiscale Gas Dynamics and MHD Turbulence Flows

Bjorn Sjogreen et al.

JOURNAL OF SCIENTIFIC COMPUTING (2020)

Article Computer Science, Interdisciplinary Applications

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

Sibusiso Mabuza et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2020)

Article Astronomy & Astrophysics

High-order magnetohydrodynamics for astrophysics with an adaptive mesh refinement discontinuous Galerkin scheme

Thomas Guillet et al.

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY (2019)

Article Mathematics

Nonlinear artificial viscosity for spectral element methods

Li Lu et al.

COMPTES RENDUS MATHEMATIQUE (2019)

Article Computer Science, Interdisciplinary Applications

Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations

Dominik Derigs et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2018)

Article Mathematics, Applied

A PROVABLY POSITIVE DISCONTINUOUS GALERKIN METHOD FOR MULTIDIMENSIONAL IDEAL MAGNETOHYDRODYNAMICS

Kailiang Wu et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2018)

Article Mathematics, Applied

SECOND-ORDER INVARIANT DOMAIN PRESERVING APPROXIMATION OF THE EULER EQUATIONS USING CONVEX LIMITING

Jean-Luc Guermond et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2018)

Article Computer Science, Interdisciplinary Applications

An FCT finite element scheme for ideal MHD equations in 1D and 2D

Melanie Basting et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2017)

Article Engineering, Multidisciplinary

Numerical investigation of a viscous regularization of the Euler equations by entropy viscosity

Murtazo Nazarov et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2017)

Article Engineering, Multidisciplinary

Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton-Krylov-AMG

J. N. Shadid et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2016)

Article Computer Science, Interdisciplinary Applications

A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes

Michael Dumbser et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2016)

Article Computer Science, Interdisciplinary Applications

Constrained hyperbolic divergence cleaning in smoothed particle magnetohydrodynamics with variable cleaning speeds

Terrence S. Tricco et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2016)

Article Mathematics, Applied

INVARIANT DOMAINS AND FIRST-ORDER CONTINUOUS FINITE ELEMENT APPROXIMATION FOR HYPERBOLIC SYSTEMS

Jean-Luc Guermond et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2016)

Article Computer Science, Interdisciplinary Applications

Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

Simone Marras et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2015)

Article Engineering, Multidisciplinary

A maximum-principle preserving C0 finite element method for scalar conservation equations

Jean-Luc Guermond et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2014)

Article Computer Science, Interdisciplinary Applications

Dispersive behaviour of high order finite element schemes for the one-way wave equation

Mark Ainsworth

JOURNAL OF COMPUTATIONAL PHYSICS (2014)

Article Computer Science, Interdisciplinary Applications

Multidimensional HLLC Riemann solver for unstructured meshes - With application to Euler and MHD flows

Dinshaw S. Balsara et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2014)

Article Mathematics, Applied

VISCOUS REGULARIZATION OF THE EULER EQUATIONS AND ENTROPY PRINCIPLES

Jean-Luc Guermond et al.

SIAM JOURNAL ON APPLIED MATHEMATICS (2014)

Article Mathematics, Applied

Convergence of a residual based artificial viscosity finite element method

Murtazo Nazarov

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2013)

Article Computer Science, Interdisciplinary Applications

Residual-based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods

Murtazo Nazarov et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS (2013)

Article Computer Science, Interdisciplinary Applications

A matrix free implicit scheme for solution of resistive magneto-hydrodynamics equations on unstructured grids

H. Sitaraman et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2013)

Article Computer Science, Interdisciplinary Applications

On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics

Santiago Badia et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2013)

Article Computer Science, Interdisciplinary Applications

Positivity-preserving DG and central DG methods for ideal MHD equations

Yue Cheng et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2013)

Article Computer Science, Interdisciplinary Applications

Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field

Fengyan Li et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2011)

Article Computer Science, Interdisciplinary Applications

Entropy viscosity method for nonlinear conservation laws

Jean-Luc Guermond et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2011)

Article Computer Science, Interdisciplinary Applications

An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations

Christiane Helzel et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2011)

Article Computer Science, Interdisciplinary Applications

Multidimensional HLLE Riemann solver: Application to Euler and magnetohydrodynamic flows

Dinshaw S. Balsara

JOURNAL OF COMPUTATIONAL PHYSICS (2010)

Article Astronomy & Astrophysics

ATHENA: A NEW CODE FOR ASTROPHYSICAL MHD

James M. Stone et al.

ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES (2008)

Article Mathematics

Entropy-based nonlinear viscosity for Fourier approximations of conservation laws

Jean-Luc Guermond et al.

COMPTES RENDUS MATHEMATIQUE (2008)

Article Mathematics, Applied

A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: theoretical framework

Francois Bouchut et al.

NUMERISCHE MATHEMATIK (2007)

Article Mathematics, Applied

An unstaggered, high-resolution constrained transport method for magnetohydrodynamic flows

James A. Rossmanith

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2006)

Article Mathematics, Applied

Locally divergence-free discontinuous Galerkin methods for MHD equations

FY Li et al.

JOURNAL OF SCIENTIFIC COMPUTING (2005)

Article Computer Science, Interdisciplinary Applications

Non-oscillatory central schemes for one- and two-dimensional MHD equations:: I

J Balbás et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2004)

Article Computer Science, Interdisciplinary Applications

Hyperbolic divergence cleaning for the MHD equations

A Dedner et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2002)

Article Computer Science, Interdisciplinary Applications

The del•B=0 constraint in shock-capturing magnetohydrodynamics codes

G Tóth

JOURNAL OF COMPUTATIONAL PHYSICS (2000)