A two-dimensional HLLC Riemann solver for conservation laws: Application to Euler and magnetohydrodynamic flows

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• 作者：Dinshaw S. Balsara
• 关键词：Higher order Godunov schemes ; Multidimensional Riemann solvers ; HLL ; HLLC ; Conservation laws ; Euler equations ; MHD
• 刊名：Journal of Computational Physics
• 出版年：2012
• 出版时间：15 September, 2012
• 年：2012
• 卷：231
• 期：22
• 页码：7476-7503
• 全文大小：2484 K

文摘

The Riemann solver presented here is general and can work with any system of conservation laws. We also present a second order accurate Godunov scheme that works in three dimensions and is entirely based on the present multidimensional HLLC Riemann solver technology. The methods presented are cost-competitive with traditional higher order Godunov schemes.

The two-dimensional HLLC Riemann solver is shown to work robustly for Euler and Magnetohydrodynamic (MHD) flows. Several stringent test problems are presented to show that the inclusion of genuinely multidimensional effects into higher order Godunov schemes indeed produces some very compelling advantages. For two dimensional problems, we were routinely able to run simulations with CFL numbers of ¡«0.7, with some two-dimensional simulations capable of reaching higher CFL numbers. For three dimensional problems, CFL numbers as high as ¡«0.6 were found to be stable. We show that on resolution-starved meshes, the scheme presented here outperforms unsplit second order Godunov schemes that are based on conventional one-dimensional Riemann solver technology. Strong discontinuities are shown to propagate very isotropically using the methods presented here. The present Riemann solver provides an elegant resolution to the problem of obtaining multi-dimensionally upwinded electric fields in MHD without resorting to a doubling of the dissipation in each dimension.