Exact Riemann solver for ideal magnetohydrodynamics that can handle all types of intermediate shocks and switch-on/off waves
Exact Riemann solver for ideal magnetohydrodynamics that can handle all types of intermediate shocks and switch-on/off waves
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DOI：
10.1017/s0022377813001268
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发表时间：
2013-10
影响因子：
2.5
通讯作者：
K. Takahashi;S. Yamada
中科院分区：
文献类型：
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作者：
K. Takahashi;S. Yamada
摘要我们建立了一个程序，可以在任意初始条件下得到理想磁流体力学（MHD）中黎曼问题的精确解。该程序不仅可以处理规则波，而且可以处理开关稀疏波和所有类型的非规则波：中间波和开关波。此外，尽管该代码部分基于Torrilhon（2002）（Torrilhon，M. 2002理想磁流体力学黎曼问题的精确解和唯一性条件。Research report 2002 - 06，Seminar for Applied Mathematics，ETH，苏黎世，瑞士），它不能处理所有类型的非规则波，也不能处理没有正常或横向磁场的初始条件。我们的求解器可以找到一个给定的黎曼问题的所有解决方案，因此，如本文所示，可以详细研究的结构的解决方案空间。因此，求解器是解决MHD Riemann问题解的存在唯一性这一突出问题的有力工具。此外，求解器可能会被应用到数值MHD格式，如Goddom计划在未来。
Abstract We have built a code to obtain the exact solutions of Riemann problems in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition. The code can handle not only regular waves but also switch-on/off rarefactions and all types of non-regular shocks: intermediate shocks and switch-on/off shocks. Furthermore, the initial conditions with vanishing normal or transverse magnetic fields can be handled, although the code is partly based on the algorithm proposed by Torrilhon (2002) (Torrilhon, M. 2002 Exact solver and uniqueness condition for Riemann problems of ideal magnetohydrodynamics. Research report 2002-06, Seminar for Applied Mathematics, ETH, Zurich, Switzerland), which cannot deal with all types of non-regular waves nor the initial conditions without normal or transverse magnetic fields. Our solver can find all the solutions for a given Riemann problem, and hence, as demonstrated in this paper, one can investigate the structure of the solution space in detail. Therefore, the solver is a powerful instrument to solve the outstanding problem of existence and uniqueness of solutions of MHD Riemann problems. Moreover, the solver may be applied to numerical MHD schemes like the Godunov scheme in the future.