相对论MHD的五波HLL黎曼解
A five-wave HLL Riemann solver for relativistic MHD
摘要：
提出了理想相对论磁流体力学方程的五波黎曼解。我们的求解器可以被看作是一个相对论性的扩展五波HLLD黎曼求解器最初开发的Miyoshi和草野理想MHD方程。黎曼问题的解近似为五波模式，由两个最外面的快速激波，两个旋转间断和中间的接触面组成。所提出的计划是相当复杂的比在经典的情况下，因为正常的速度不再是恒定的旋转模式。尽管如此，通过求解总压变量中的非线性标量方程，可以得到对兰金-雨果尼奥跳跃条件的适当封闭，对于所选的配置，总压变量在整个黎曼风扇上必须是常数。新的黎曼解算器的精度进行了验证，对一维测试和多维应用。结果表明，我们的新的求解器大大提高了流行的HLL求解器或最近提出的HLLC计划。
英文摘要：
We present a five-wave Riemann solver for the equations of ideal relativistic magnetohydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi and Kusano for the equations of ideal MHD. The solution to the Riemann problem is approximated by a five wave pattern, comprised of two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a nonlinear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular HLL solver or the recently proposed HLLC schemes.
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