Numerical solution of shallow water magnetohydrodynamic equations with non-flat bottom topography

DOI10.1080/10618562.2014.891019OpenAlexW2028800647MaRDI QIDQ5071751

Munshoor Ahmed, Shamsul Qamar, Saqib Zia

Publication date: 22 April 2022

Published in: International Journal of Computational Fluid Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10618562.2014.891019

zbMATH Keywords

conservation lawsprojection methoddiscontinuous solutionskinetic flux vector splitting schemebottom topographycentral-upwind schemeshallow water magnetohydrodynamic equations

Mathematics Subject Classification ID

Fluid mechanics (76-XX) Geophysics (86-XX)

Related Items (5)

High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics ⋮ On the well-posedness of strong solution to ideal magnetohydrodynamic equations ⋮ A new S-M limiter entropy stable scheme based on moving mesh method for ideal MHD and SWMHD equations ⋮ A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes ⋮ Asymptotic shallow models arising in magnetohydrodynamics

Cites Work

• Unnamed Item
• A kinetic flux-vector splitting method for the shallow water magnetohydrodynamics
• A gas-kinetic scheme for shallow-water equations with source terms
• The effect of nonzero \(\bigtriangledown\cdot B\) on the numerical solution of the magnetohydrodynamic equations
• Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
• Kinetic flux vector splitting for Euler equations
• The \(\nabla \cdot B=0\) constraint in shock-capturing magnetohydrodynamics codes
• A well-balanced gas-kinetic scheme for the shallow-water equations with source terms
• An evolution Galerkin scheme for the shallow water magnetohydrodynamic equations in two space dimensions
• A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics
• Gas-kinetic theory-based flux splitting method for ideal magnetohydrodynamics
• A solution-adaptive upwind scheme for ideal magnetohydrodynamics
• Numerical simulation of the MHD equations by a kinetic-type method
• New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system
• High order finite difference WENO schemes with the exact conservation property for the shallow water equations
• Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
• A steady-state capturing method for hyperbolic systems with geometrical source terms
• Adaptive multi-resolution central-upwind schemes for systems of conservation laws
• Non-oscillatory central-upwind scheme for hyperbolic conservation laws
• Rossby waves in “shallow water” magnetohydrodynamics
• Genuinely multidimensional evolution Galerkin schemes for the shallow water equations

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