An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
A higher-order Godunov method for multidimensional ideal magnetohydrodynamics
SIAM Journal on Scientific Computing
Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Non-oscillatory central schemes for one- and two-dimensional MHD equations: I
Journal of Computational Physics
Journal of Computational Physics
Central finite volume methods with constrained transport divergence treatment for ideal MHD
Journal of Computational Physics
Journal of Computational Physics
Applied Numerical Mathematics
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We propose an unstaggered, non-oscillatory, second-order accurate central scheme for approximating the solution of general hyperbolic systems in one and two space dimensions, and in particular for estimating the solution of ideal magnetohydrodynamic problems and shallow water magnetohydrodynamic problems. In contrast with standard central schemes that evolve the numerical solution on two staggered grids at consecutive time steps, the method we propose evolves the numerical solution on a single unique grid, and avoids the resolution of the Riemann problems arising at the cell interfaces thanks to a layer of ghost staggered cells implicitly used while updating the numerical solution on the control cells. To satisfy the divergence-free constraint of the magnetic field/flux in the numerical solution of ideal/shallow water magnetohydrodynamic problems, we adapt Evans and Hawley's constrained transport method to our unstaggered base scheme and use it to correct the magnetic field/flux components at the end of each time step. The resulting method is used to solve classical ideal/shallow water magnetohydrodynamic problems; the obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the efficiency and the potential of the proposed method.