Positivity-Preserving Finite Difference Weighted ENO Schemes with Constrained Transport for Ideal Magnetohydrodynamic Equations

DOI10.1137/140971208zbMath1329.76225arXiv1406.5098OpenAlexW2963562886MaRDI QIDQ5266122

Qi Tang, Yuan Liu, Zhengfu Xu, Andrew J. Christlieb

Publication date: 30 July 2015

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.5098

zbMATH Keywords

finite differenceshyperbolic conservation lawsmagnetohydrodynamicspositivity-preservingconstrained transportWENO

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Finite difference methods applied to problems in fluid mechanics (76M20) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Magnetohydrodynamics and electrohydrodynamics (76W05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

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Cites Work

• Unnamed Item
• A parametrized maximum principle preserving flux limiter for finite difference RK-WENO schemes with applications in incompressible flows
• Finite difference weighted essentially non-oscillatory schemes with constrained transport for ideal magnetohydrodynamics
• Positivity-preserving method for high-order conservative schemes solving compressible Euler equations
• Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations
• An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations
• Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field
• Locally divergence-free discontinuous Galerkin methods for MHD equations
• A central-constrained transport scheme for ideal magnetohydrodynamics
• On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
• High order parametrized maximum-principle-preserving and positivity-preserving WENO schemes on unstructured meshes
• Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magneto\-hydrodynamics
• A positive MUSCL-Hancock scheme for ideal magnetohydrodynamics
• The effect of nonzero \(\bigtriangledown\cdot B\) on the numerical solution of the magnetohydrodynamic equations
• Maintaining pressure positivity in magnetohydrodynamic simulations
• A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations
• A simple finite difference scheme for multidimensional magnetohydrodynamical equations
• A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
• On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method.
• A positive conservative method for magnetohydrodynamics based on HLL and Roe methods
• The \(\nabla \cdot B=0\) constraint in shock-capturing magnetohydrodynamics codes
• A solution-adaptive upwind scheme for ideal magnetohydrodynamics
• Efficient implementation of weighted ENO schemes
• A second-order unsplit Godunov scheme for cell-centered MHD: the CTU-GLM scheme
• An unsplit Godunov method for ideal MHD via constrained transport in three dimensions
• Parametrized maximum principle preserving flux limiters for high order schemes solving multi-dimensional scalar hyperbolic conservation laws
• Positivity-preserving DG and central DG methods for ideal MHD equations
• Parametrized positivity preserving flux limiters for the high order finite difference WENO scheme solving compressible Euler equations
• Strong Stability-Preserving High-Order Time Discretization Methods
• Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem
• An Unstaggered, High‐Resolution Constrained Transport Method for Magnetohydrodynamic Flows
• A High-Order Unstaggered Constrained-Transport Method for the Three-Dimensional Ideal Magnetohydrodynamic Equations Based on the Method of Lines
• Locally Divergence-preserving Upwind Finite Volume Schemes for Magnetohydrodynamic Equations
• Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes