A fluid-mixture type algorithm for barotropic two-fluid flow problems

Our goal is to present a simple interface-capturing approach for barotropic two-fluid flow problems in more than one space dimension. We use the compressible Euler equations in isentropic form as a model system with the thermodynamic property of each fluid component characterized by the Tait equation of state. The algorithm uses a non-isentropic form of the Tait equation of state as a basis to the modeling of the numerically induced mixing between two different barotropic fluid components within a grid cell. Similar to our previous work for multicomponent problems, see [J. Comput. Phys. 171 (2001) 678] and references cited therein, we introduce a mixture type of the model system that consists of the full Euler equations for the basic conserved variables and an additional set of evolution equations for the problem-dependent material quantities and also the approximate location of the interfaces. A standard high-resolution method based on a wave-propagation formulation is employed to solve the proposed model system with the dimensional-splitting technique incorporated in the method for multidimensional problems. Several numerical results are presented in one, two, and three space dimensions that show the feasibility of the method as applied to a reasonable class of practical problems without introducing any spurious oscillations in the pressure near the smeared material interfaces.