A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state
A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state
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DOI：
10.1006/jcph.2001.6801
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发表时间：
2001-08
影响因子：
4.1
通讯作者：
K. Shyue
中科院分区：
文献类型：
--
作者：
K. Shyue
范德华流体多分量问题的数值求解方法[j]。理论物理。[m], 156 (1999), pp. 43-88]扩展到更一般的情况下，真实材料的特征是一个Mie-Gruneisen状态方程。和以前一样，假设感兴趣的流动状态是均匀的，在分离不同流体成分的两个区域的界面上，压力和速度（它的法向分量）没有跳跃。该算法采用混合类型的模型系统，该模型系统由基本守恒变量的气体动力学欧拉方程和问题相关物理量的附加有效方程组合而成。在这种方法中，引入后一种方程主要是为了便于从状态方程计算压力，推导后一种方程是为了确保在网格单元中存在两种或更多流体组分的界面附近的能量方程建模的一致性，以及在其他单组分区域的质量方程的实现。将最初为单组分流设计的标准高分辨率波传播方法推广到多组分流系统中，从而有效地实现了算法。在一维和二维空间中给出了几个数值结果，表明该方法与Roe Riemann求解器应用于一类合理的实际问题时的可行性，而不会在界面附近的压力中引入任何伪振荡。这包括使用Berger和LeVeque的AMRCLAW软件包的多组件版本在两个空间维度上模拟水下铝板对铜板的影响所获得的结果。
Abstract A simple interface-capturing approach proposed previously by the author for efficient numerical resolution of multicomponent problems with a van der Waals fluid [ J. Comput. Phys. , 156 (1999), pp. 43–88] is extended to a more general case with real materials characterized by a Mie–Gruneisen equation of state. As before, the flow regime of interests is assumed to be homogeneous with no jumps in the pressure and velocity (the normal component of it) across the interfaces that separate two regions of different fluid components. The algorithm uses a mixture type of the model system that is formed by combining the Euler equations of gas dynamics for the basic conserved variables and an additional set of effective equations for the problem-dependent material quantities. In this approach, the latter equations are introduced in the algorithm primarily for an easy computation of the pressure from the equation of state, and are derived so as to ensure a consistent modeling of the energy equation near the interfaces where two or more fluid components are present in a grid cell, and also the fulfillment of the mass equation in the other single component regions. A standard high-resolution wave propagation method designed originally for single component flows is generalized to solve the proposed system for multicomponent flows, giving an efficient implementation of the algorithm. Several numerical results are presented in both one and two space dimensions that show the feasibility of the method with the Roe Riemann solver as applied to a reasonable class of practical problems without introducing any spurious oscillations in the pressure near the interfaces. This includes results obtained using a multicomponent version of the AMRCLAW software package of Berger and LeVeque for the simulation of the impact of an underwater aluminum plate to a copper plate in two space dimensions.