一种适用于磁流体力学切向间断的HLLC黎曼算子

磁场的存在使得磁流体力学特征波模不同于流体力学, 因此直接由流体力学HLLC黎曼算子导出的HLLC双中间态在交界的间断面会出现不守恒的问题。通常降级采用HLL单磁场中间态代替HLLC双磁场中间态以实现守恒和计算稳定, 代价是切向间断的模拟精度不足。本文对此进行改进, 在模拟切向间断时仍然保留原有的HLLC双磁场中间态, 同时各守恒量仍然能够满足Toro相容条件; 改进型HLLC算子在间断两侧的磁场分量存在差异, 因此能够更精确还原切向间断面。基于数值测试, 包括一维激波管和切向间断的时变模拟, 以及地球磁层三维数值模拟, 将模拟结果进行对比, 结果表明: 相比于已发展的HLLC算子, 改进型HLLC算子对切向间断具有更好的捕捉精度, 能够达到或接近耗时更多的HLLD算子的模拟精度。

An HLLC Riemann Solver for MHD Tangential Discontinuities

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.