An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics
Journal of Computational Physics
A higher-order Godunov method for multidimensional ideal magnetohydrodynamics
SIAM Journal on Scientific Computing
An approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Notes on the eigensystem of magnetohydrodynamics
SIAM Journal on Applied Mathematics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Gas-kinetic theory-based flux splitting method for ideal magnetohydrodynamics
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
A high-order gas-kinetic method for multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
Non-oscillatory central schemes for one- and two-dimensional MHD equations: I
Journal of Computational Physics
Solving the MHD equations by the space-time conservation element and solution element method
Journal of Computational Physics
Application of space-time CE/SE method to shallow water magnetohydrodynamic equations
Journal of Computational and Applied Mathematics
A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics
Journal of Computational Physics
The space-time CESE method for solving special relativistic hydrodynamic equations
Journal of Computational Physics
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In this article we implement a variant space-time conservation element and solution element (CE/SE) method for the numerical solution of two-dimensional ideal magnetohydrodynamic (MHD) equations. The current method uses regular rectangular mesh elements for the domain discretization in two space dimensions. In the method, a single conservation element at each grid point is employed for solving conservation laws no matter in one, two, and three space dimensions. The present scheme uses the conservation element to calculate flow variables only, while the gradients of flow variables are calculated by a central differencing reconstruction procedure. Although the present scheme does not satisfy the divergence free condition, the numerical results obtained with and without divergence cleaning procedure are almost similar. Several two-dimensional test cases are included in this manuscript. These problems are hard test cases for those numerical methods which do not satisfy the divergence free condition. Therefore, the test problems further verify the performance of proposed scheme. A comparison with central schemes shows better resolution of the CE/SE method results.