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

Abstract

The governing equations of shallow water magnetohydrodynamics describe the dynamics of a thin layer of nearly incompressible and electrically conducting fluids for which the evolution is nearly two-dimensional with magnetic equilibrium in the third direction. A high-resolution central-upwind scheme is applied to solve the model equations considering non-flat bottom topography. The suggested method is an upwind biased non-oscillatory finite volume scheme which doées not require a Riemann solver at each time step. To satisfy the divergence-free constraint, the projection method is used. Several case studies are carried out. For validation, a gas kinetic flux vector splitting scheme is also applied to the same model.

Keywords:

• shallow water magnetohydrodynamic equations
• central-upwind scheme
• kinetic flux vector splitting scheme
• projection method
• bottom topography
• conservation laws
• discontinuous solutions

Additional information

Funding

This work is partially supported by the Higher Education Commission (HEC) of Pakistan through grant No. 1375.