A Simple Method for Compressible Multifluid Flows
A Simple Method for Compressible Multifluid Flows
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DOI：
10.1137/s1064827597323749
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发表时间：
1999-11
期刊：
影响因子：
--
通讯作者：
R. Saurel;R. Abgrall
中科院分区：
文献类型：
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作者：
R. Saurel;R. Abgrall
本文提出了一种简单的二阶精度全欧拉数值方法，用于模拟流体动力学区域中由加强气体状态方程控制的多流体可压缩流动。我们的数值方法依赖于一个二阶Godunov型计划，与近似的黎曼解的守恒方程的分辨率，和一组非保守方程。它对所有网格点都有效，并允许接口的分辨率。这种方法适用于任意数量的界面，用于分裂和合并。它允许非常高的密度比（高达1000）。它能够计算非常强的冲击波（压力比高达10 5）。与现有的所有方案（将界面视为不连续）相反，该方法将界面视为数值扩散区，因为在可压缩单相流中计算接触不连续性，但描述混合区的变量与密度，动量和能量一致。在一维、二维和三维中提出了几个测试问题。例如，这种方法允许计算在液体中传播的冲击波与气瓶的相互作用，以及Richtmeyer-Meshkov不稳定性，或超高速碰撞，具有现实的初始条件。我们说明我们的方法与Rusanov通量。然而，同样的原理可以应用于更一般的一类方案。
A simple second order accurate and fully Eulerian numerical method is presented for the simulation of multifluid compressible flows, governed by the stiffened gas equation of state, in hydrodynamic regime. Our numerical method relies on a second order Godunov-type scheme, with approximate Riemann solver for the resolution of conservation equations, and a set of nonconservative equations. It is valid for all mesh points and allows the resolution of interfaces. This method works for an arbitrary number of interfaces, for breakup and coalescence. It allows very high density ratios (up to 1000). It is able to compute very strong shock waves (pressure ratio up to 10 5). Contrary to all existing schemes (which consider the interface as a discontinuity) the method considers the interface as a numerical diffusion zone as contact discontinuities are computed in compressible single phase flows, but the variables describing the mixture zone are computed consistently with the density, momentum and energy. Several test problems are presented in one, two, and three dimensions. This method allows, for example, the computation of the interaction of a shock wave propagating in a liquid with a gas cylinder, as well as Richtmeyer--Meshkov instabilities, or hypervelocity impact, with realistic initial conditions. We illustrate our method with the Rusanov flux. However, the same principle can be applied to a more general class of schemes.