An HLLC Riemann Solver for MHD Tangential Discontinuities

doi:10.19596/j.cnki.1001-246x.8426

Abstract

Abstract:

Compared with those of hydrodynamics, the existence of magnetic field leads to extra characteristic waves for magnetohydrodynamics (MHD), and further leads to an inconsistency of jump condition across the contact discontinuity. Usually, for the magnetic field variables in an HLLC Riemann solver, a single HLL intermediate state is used to replace two HLLC intermediate states to achieve conservation and computational stability, at the cost of insufficient simulation accuracy for tangential discontinuity. In this paper, a previouly developed HLLC solver is specially constructed to deal with MHD tangential discontinuities accurately and satisfy the so-called Toro condition. With numerical tests, such as the time-dependent simulation of one-dimensional shock tube, the tangential discontinuities, and the global MHD simulation of Earth's magnetosphere, we compare numerical results of the modified HLLC solver with those of the standard HLLC and HLLD solvers. It indicates that the modified HLLC solver has better capture accuracy for tangential discontinuities than the previously developed HLLC solver, and has the accuracy of the more time-consuming HLLD solver in some situations.

Key words: magnetohydrodynamics, Riemann solver, HLLC, tangential discontinuities

Xinyue XI, Xiaocheng GUO, Chi WANG. An HLLC Riemann Solver for MHD Tangential Discontinuities[J]. Chinese Journal of Computational Physics, 2022, 39(3): 286-296.

Figures/Tables 6

Fig.1 HLL Riemann fan in x-t plane, showing left state Ul, right state Ur, and middle state U*

Fig.2 HLLC Riemann fan in x-t plane, showing left state Ul, right state Ur, and middle states Ul* and Ur*

Fig.3 Evolution of one-dimensional MHD shocktube

Fig.4 Simulation of a tangential discontinuity for the case of pressure jump across the discontinuity: Spatial profiles of density N, pressure p, velocity component Ux and magnetic field component By

Fig.5 Simulation of a tangential discontinuity for the case of constant pressure across the discontinuity: Spatial profiles of density N, pressure p, velocity component Ux and magnetic field component By

Fig.6 Pressure contours of magnetosphere in equatorial plane (x-z) with three Riemann solvers (a) HLLC-L, (b) HLLC-R, (c) HLLD, and (d) pressure profiles along the Sun-Earth line

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