An unconventional divergence preserving finite-volume discretization of Lagrangian ideal MHD

DOI10.1007/s42967-023-00309-2MaRDI QIDQ6593775

Pierre-Henri Maire, Walter Boscheri, Raphaël Loubère

Publication date: 27 August 2024

Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

hyper-elasticitymoving unstructured meshesideal magnetohydrodynamics (MHD) equationsa posteriori MOOD limitingcell-centered Lagrangian finite-volume (FV) schemes

Mathematics Subject Classification ID

Magnetohydrodynamics and electrohydrodynamics (76W05) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Waves in compressible fluids (76N30)

Cites Work

• Unnamed Item
• Unnamed Item
• Handbook of numerical methods for hyperbolic problems. Basic and fundamental issues
• A direct arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D
• A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids
• Multidimensional Riemann problem with self-similar internal structure. I: Application to hyperbolic conservation laws on structured meshes
• Direct arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws
• A high-order finite volume method for systems of conservation laws-multi-dimensional optimal order detection (MOOD)
• High-order WENO schemes: Investigations on non-uniform convergence for MHD Riemann problems
• An HLLC Riemann solver for magneto-hydrodynamics
• Arbitrary Lagrangian-Eulerian methods for modeling high-speed compressible multimaterial flows
• The internal consistency, stability, and accuracy of the discrete, compatible formulation of Lagrangian hydrodynamics
• An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
• A multiwave approximate Riemann solver for ideal MHD based on relaxation. II: Numerical implementation with 3 and 5 waves
• Splitting based finite volume schemes for ideal MHD equations
• A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes
• An upwind differencing scheme for the equations of ideal magnetohydrodynamics
• The effect of nonzero \(\bigtriangledown\cdot B\) on the numerical solution of the magnetohydrodynamic equations
• A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations
• A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
• Positive and entropy-stable Godunov-type schemes for gas dynamics and MHD equations in Lagrangian or Eulerian coordinates
• Non-uniform convergence of finite volume schemes for Riemann problems of ideal magnetohydrodynamics
• The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I: The scalar case
• Hyperbolic divergence cleaning for the MHD equations
• Ideal GLM-MHD: about the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations
• A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics
• An unsplit Godunov method for ideal MHD via constrained transport
• A solution-adaptive upwind scheme for ideal magnetohydrodynamics
• A 3D cell-centered Lagrangian scheme for the ideal magnetohydrodynamics equations on unstructured meshes
• A 3D cell-centered ADER MOOD finite volume method for solving updated Lagrangian hyperelasticity on unstructured grids
• A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids
• Multidimensional HLLE Riemann solver: application to Euler and magnetohydrodynamic flows
• Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes
• Cell-centered discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics
• A 3D GCL compatible cell-centered Lagrangian scheme for solving gas dynamics equations
• A two-dimensional HLLC Riemann solver for conservation laws: application to Euler and magnetohydrodynamic flows
• A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: Theoretical framework
• Derivative Riemann solvers for systems of conservation laws and ader methods
• High-order curvilinear finite element magneto-hydrodynamics. I: A conservative Lagrangian scheme
• A NEW LAGRANGIAN FORMULATION OF IDEAL MAGNETOHYDRODYNAMICS
• On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
• Numerical Methods for Eulerian and Lagrangian Conservation Laws
• A RKDG Method for 2D Lagrangian Ideal Magnetohydrodynamics Equations with Exactly Divergence-Free Magnetic Field
• Approximate Riemann Solvers and Robust High-Order Finite Volume Schemes for Multi-Dimensional Ideal MHD Equations
• Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes

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