Regular Article: A Fluid-Mixture Type Algorithm for Compressible Multicomponent Flow with van der Waals Equation of State
Regular Article: A Fluid-Mixture Type Algorithm for Compressible Multicomponent Flow with van der Waals Equation of State
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DOI：
10.1006/jcph.1999.6349
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发表时间：
1999-11
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
在作者以前的工作中，一个简单的界面捕捉方法已被开发和验证的可压缩多组分流动与加劲气体状态方程在多个空间维度。该算法使用一个混合类型的模型方程写在一个准保守的形式，以确保一致的近似的能量方程附近的界面，其中两个或两个以上的流体成分存在于一个网格单元。一个标准的高分辨率波传播方法来解决所提出的系统，给出了一个有效的实现算法。在本文中，该方法被扩展到一个更一般的两相（液-气）流的兴趣的流体的特点是由一个货车范德华型状态方程。几个数值结果在一个和两个空间维度，显示的可行性的方法与Roe求解器应用于实际问题，而不引入任何寄生振荡的压力附近的接口。这包括一个收敛研究的冲击波在液体中的气泡。为了处理一个困难的滑移线问题，有一个强剪切流沿沿着界面移动，我们实现的方法的基础上，只有冲击黎曼求解器与一个额外的更新计划的总动能。而不是使用的解决方案，从基本守恒定律的密度和动量，招致大的误差，由此产生的总动能是用来计算的压力状态方程，产生通常更准确的结果比未经修改的方法附近的滑移线。这是证明了一些样本二维黎曼问题的数值结果。
In previous work by the author, a simple interface-capturing approach has been developed and validated for compressible multicomponent flows with a stiffened gas equation of state in multiple space dimensions. The algorithm uses a mixture type of the model equations written in a quasi-conservative form to ensure a consistent approximation of the energy equation near the interfaces where two or more fluid components are present in a grid cell. A standard high-resolution wave propagation method is employed to solve the proposed system, giving an efficient implementation of the algorithm. In this paper, the method is extended to a more general two-phase (liquid-gas) flow where the fluid of interests is characterized by a van der Waals-type equation of state. Several numerical results are presented in both one and two space dimensions that show the feasibility of the method with the Roe solver as applied to practical problems without introducing any spurious oscillations in the pressure near the interfaces. This includes a convergence study of a shock wave in liquid over a gas bubble. To deal with a difficult slip line problem where there is a strong shear flow moving along the interface, we implement the method based on the shock-only Riemann solver with an additional update by the scheme to the total kinetic energy. Rather than using solutions from the basic conservation laws for the density and momenta which incurs large errors, the resulting total kinetic energy is used to the computation of the pressure from the equation of state, yielding typically more accurate results than the unmodified method near the slip lines. This is demonstrated by numerical results of some sample two-dimensional Riemann problems.