A fluid-mixture type algorithm for compressible multicomponent flow with van der Waals equation of state

In previous work by the author, a simple interface-capturing approach has b een developed and validated for compressible multicomponent flows with a st iffened gas equation of state in multiple space dimensions, The algorithm u ses a mixture type of the model equations written in a quasi-conservative f orm to ensure a consistent approximation of the energy equation near the in terfaces where two or more fluid components are present in a grid cell. A s tandard high-resolution wave propagation method is employed to solve the pr oposed system, giving an efficient implementation of the algorithm. In this paper, the method is extended to a more general two-phase (liquid-gas) flo w where the fluid of interests is characterized by a van der Waals-type equ ation of state. Several numerical results are presented in both one and two space dimensions that show the feasibility of the method with the Roe solv er as applied to practical problems without introducing any spurious oscill ations in the pressure near the interfaces, This includes a convergence stu dy of a shock wave in liquid over a gas bubble. To deal with a difficult sl ip line problem where there is a strong shear flow moving along the interfa ce, 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 us ing solutions from the basic conservation laws for the density and momenta which incurs large errors, the resulting total kinetic energy is used to th e computation of the pressure from the equation of state, yielding typicall y more accurate results than the unmodified method near the slip lines. Thi s is demonstrated by numerical results of some sample two-dimensional Riema nn problems. (C) 1999 Academic Press.