Implementation of the HLL-GRP solver for multidimensional ideal MHD simulations based on finite volume method

Abstract

The HLL solver for the generalized Riemann problem (HLL-GRP solver) is attractive because it is easy to implement for 1D hyperbolic problems and performs well. Based on the rotational invariance of multidimensional magnetohydrodynamics (MHD) equations, this paper provides a means of implementing the 1D HLL-GRP solver into the multidimensional ideal MHD simulations within the framework of the finite volume method. Furthermore, the Godunov-Powell source term and the locally divergence-free WLS-ENO reconstruction are adopted to constrain the divergence of the magnetic field. To maintain positive density and pressure, a positivity-preserving (PP) limiter is performed on the reconstructed polynomials of density and pressure. Some comparisons with other methods are listed in 1D, 2D and 3D MHD benchmark cases. The numerical results demonstrate that the scheme is stable and can well control the divergence of the magnetic field.