In many situations, the equations of state (EOS) found in the literature have only a limited range of validity. Besides, different types of EOS are required for different fluids of compressible multi-fluid flows. These inspire us to investigate compressible multi-fluid flows with different types of equation of state (EOS). In this paper, the oscillation-free adaptive method for compressible two-fluid flows with different types of equation of state (EOS) is proposed. By using a general form of EOS instead of solving the non-linear equation, the pressure of the mixture can be analytically calculated for compressible multi-fluid flows with different types of EOS. It is proved that it preserves the oscillation-free property across the interface. To capture the interface as fine as sharp interface, the quadrilateral-cell based adaptive mesh is employed. In this adaptive method, the cells with different levels are stored in different lists. This avoids the recursive calculation of solution of mother (non-leaf) cells. Moreover, the edges are separated stored into two lists for leaf edges and non-leaf edges respectively. Hence, there is no need to handle the handing nodes and no special treatment at the interface between the finer cell and the coarse cell. Thus, high efficiency is obtained due to these features. To examine its performance in solving the various compressible two-fluid flow problems with two different types of EOS, the interface translation and bubble shock interaction case with different types of EOS are employed. The results show that it can adaptively and accurately solve these problems and especially preserve the oscillation-free property of pressure and velocity across the material interface.
Zheng HW,Shu C,Chew YT,et al. Oscillation-free adaptive simulation of compressible two-fluid flows with different types of equation of state[C]NEW APPROACHES IN MODELING MULTIPHASE FLOWS AND DISPERSION IN TURBULENCE, FRACTAL METHODS AND SYNTHETIC TURBULENCE,2012:103-117.