Application of space-time CE/SE method to shallow water magnetohydrodynamic equations

DOI10.1016/j.cam.2005.08.014zbMath1168.76385OpenAlexW2085689902MaRDI QIDQ2499800

Shamsul Qamar, Gerald Warnecke

Publication date: 14 August 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.08.014

zbMATH Keywords

conservation lawshyperbolic systemsdiscontinuous solutionsCE/SE methodshallow water magnetohydrodynamic equations

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Magnetohydrodynamics and electrohydrodynamics (76W05) Initial value problems for first-order hyperbolic systems (35L45)

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High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics ⋮ The space-time CE/SE method for solving single and two-phase shallow flow models ⋮ Improved CE/SE scheme with particle level set method for numerical simulation of spall fracture due to high-velocity impact ⋮ A multi well-balanced scheme for the shallow water MHD system with topography ⋮ The space-time CESE method for solving special relativistic hydrodynamic equations ⋮ A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes ⋮ Transport of pollutant in shallow flows: a space-time CE/SE scheme ⋮ The space-time CESE scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients ⋮ Roe-type schemes for shallow water magnetohydrodynamics with hyperbolic divergence cleaning ⋮ On the application of a variant CE/SE method for solving two-dimensional ideal MHD equations ⋮ Robust high-order space-time conservative schemes for solving conservation laws on hybrid meshes ⋮ Two-dimensional dual-phase-lag thermal behavior in single-/multi-layer structures using CESE method ⋮ The space-time CE/SE method for solving one-dimensional special relativistic magnetohydrodynamics equations

Cites Work

• The effect of nonzero \(\bigtriangledown\cdot B\) on the numerical solution of the magnetohydrodynamic equations
• The \(\nabla \cdot B=0\) constraint in shock-capturing magnetohydrodynamics codes
• An evolution Galerkin scheme for the shallow water magnetohydrodynamic equations in two space dimensions
• The method of space-time conservation element and solution element -- a new approach for solving the Navier-Stokes and Euler equations
• The space-time conservation element and solution element method: A new high-resolution and genuinely multidimensional paradigm for solving conservation laws
• Genuinely multidimensional evolution Galerkin schemes for the shallow water equations
• A space-time conservation element and solution element method for solving the two- and three-dimensional unsteady Euler equations using quadilateral and hexahedral meshes.

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