A Fluid-Mixture Type Algorithm for Compressible Multicomponent Flow with van der Waals Equation of State

✍ Scribed by Keh-Ming Shyue

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 477 KB
• Volume: 156
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1999.6349

✦ Synopsis

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 Waalstype 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.