DISPATCH方法：一种用于理想磁流体动力学的近似、基于熵的黎曼求解器
DISPATCH methods: an approximate, entropy-based Riemann solver for ideal magnetohydrodynamics
AI总结：
本文提出DISPATCH方法，将Godunov型HLLD黎曼求解器改用熵作为主要热力学变量，以在宽马赫数范围内维持流体静力学平衡，并通过标准测试验证其有效性。
摘要：
随着超级计算机的发展，我们现在能够进行尺度范围非常大的模拟。在天体物理应用中，例如模拟太阳、恒星和行星大气、星际介质等，气体压力、密度、温度、等离子体β、马赫数、雷诺数等物理量可以相差多个数量级。这需要一个稳健的求解器，能够处理非常广泛的条件范围，并在适用的情况下维持流体静力学平衡。我们重新构造了一种Godunov型HLLD黎曼求解器，使其适用于大气应用中在一系列马赫数范围内维持流体静力学平衡，适用于动能和磁能主导热能而无需任何临时修正的工况。我们改变求解器，使用熵而不是总能量作为MHD方程组中的主要热力学变量。熵并不守恒，当动能和磁能转化为热量时，熵会增加，这是符合物理规律的。我们提出使用一种近似的、基于熵的黎曼求解器，作为已被广泛使用的黎曼求解器公式的替代方案，在可能有益的情况下使用。我们进行了一系列不同条件下的标准测试，并表明新的Godunov型黎曼求解器公式是有效的且具有前景。
英文摘要：
With the advance of supercomputers we can now afford simulations with very large ranges of scales. In astrophysical applications, e.g. simulating Solar, stellar and planetary atmospheres, interstellar medium, etc; physical quantities, like gas pressure, density, temperature, plasma $β$, Mach, Reynolds numbers can vary by orders of magnitude. This requires a robust solver, which can deal with a very wide range of conditions and be able to maintain hydrostatic equilibrium where it is applicable. We reformulate a Godunov-type HLLD Riemann solver that it would be suitable to maintain hydrostatic equilibrium in atmospheric applications in a range of Mach numbers, regimes where kinetic and magnetic energies dominate over thermal energy without any ad-hoc corrections. We change the solver to use entropy instead of total energy as the primary thermodynamic variable in the system of MHD equations. The entropy is not conserved, it increases when kinetic and magnetic energy is converted to heat, as it should. We propose using an approximate entropy - based Riemann solver as an alternative to already widely used Riemann solver formulations where it might be beneficial. We conduct a series of standard tests with varying conditions and show that the new formulation for the Godunov type Riemann solver works and is promising.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
