A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics
A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics
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DOI：
10.1016/j.jcp.2005.02.017
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发表时间：
2005-09-01
影响因子：
4.1
通讯作者：
Kusano, K
中科院分区：
文献类型：
--
作者：
Miyoshi, T;Kusano, K
基于Riemann扇面上法向速度恒定的假设，发展了一种新的多态Harten-Lax-van Leer(HLL)近似黎曼解算器，用于求解理想磁流体力学方程。这一假设与欧拉方程的HLLC(“C”表示接触)近似黎曼求解器中所用的相同。根据这个假设，自然地推导出当B-x不等于0时，Riemann扇应该由四个中间态组成，而当B-x=0时，中间态的数目减少到两个。由于这种近似黎曼系统满足所有跳跃条件的中间态都是解析的，所以可以直接构造多态HLL黎曼求解器。结果表明，这种求解器可以精确地求解MHD系统中形成的孤立不连续面，因此被称为HLLD黎曼求解器。(在这里，“D”代表不连续。)分析证明了HLLD黎曼求解器与HLLC黎曼求解器一样是正守恒的。实际上，当磁场消失时，HLLD黎曼解算器与HLLC黎曼解算器相对应。数值试验表明，HLLD黎曼求解器比线性化黎曼求解器具有更强的鲁棒性和更高的效率，其分辨率也是一样好的。这表明，对于理想的MHD方程，HLLD求解器在实际应用中一定是有用的。(C)2005 Elsevier Inc.保留所有权利。
A new multi-state Harten-Lax-van Leer (HLL) approximate Riemann solver for the ideal magnetohydrodynamic (MHD) equations is developed based on the assumption that the normal velocity is constant over the Riemann fan. This assumption is same as that used in the HLLC ("C" denotes Contact) approximate Riemann solver for the Euler equations. From the assumption, it is naturally derived that the Riemann fan should consist of four intermediate states for B-x not equal 0, whereas the number of the intermediate states is reduced to two when B-x = 0. Since the intermediate states satisfied with all jump conditions in this approximate Riemann system are analytically obtained, the multi-state HLL Riemann solver can be constructed straightforwardly. It is shown that this solver can exactly resolve isolated discontinuities formed in the MHD system, and hence named as HLLD Riemann solver. (Here, "D" stands for Discontinuities.) It is also analytically proved that the HLLD Riemann solver is positively conservative like the HLLC Riemann solver. Indeed, the HLLD Riemann solver corresponds to the HLLC Riemann solver when the magnetic field vanishes. Numerical tests demonstrate that the HLLD Riemann solver is more robust and efficient than the linearized Riemann solver, and its resolution is equally good. It indicates that the HLLD solver must be useful in practical applications for the ideal MHD equations. (c) 2005 Elsevier Inc. All rights reserved.