Proceedings of Symposia in Applied Mathematics 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 cen-tral schemes that alternate the numerical solution on two staggered grids, the method we propose evolves the numerical solution on a single, but uses im-plicitly ghost staggered cells to bypass the resolution of the Riemann problems arising at the cell interfaces. To ensure an admissible physical solution when solving MHD/SMHD problems, we adapt the constrained transport method and apply it to our unstaggered central schemes.We numerically solve classi-cal problems in astrophysics using the UCS method; the solenoidal property is satis¯ed 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 con¯rming the ef-¯ciency and potential of the scheme. 1