Unstaggered central schemes for MHD and SMHD

Abstract

We develop second-order nonoscillatory unstaggered central schemes (UCS) with a constrained transport-type method to solve one and two-dimensional hyperbolic problems arising in astrophysics. In contrast with the original central schemes that alternate the numerical solution on two staggered grids, the method we propose evolves the numerical solution on a single, but uses implicitly ghost staggered cells to bypass the resolution of the Riemann problemsarising at the cell interfaces. To ensure an admissible physical solution whensolving MHD/SMHD problems, we adapt the constrained transport methodand apply it to our unstaggered central schemes.We numerically solve classical problems in astrophysics using the UCS method; the solenoidal property is satisfied at the discrete level thanks to the adapted constrained transport method and the obtained numerical results are in good agreement with their corresponding ones appearing in the recent literature, thus confirming the efficiency and potential of the scheme