OPEN ACCESS AM A Gas-Kinetic Scheme for Six-Equation Two-Phase Flow Model

Copyright © 2014 Saqib Zia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accordance of the Creative Commons Attribution License all Copyrights © 2014 are reserved for SCIRP and the owner of the intellectual property Saqib Zia et al. All Copyright © 2014 are guarded by law and by SCIRP as a guardian. A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features of the model are that it is hyperbolic with only three wave propagation speeds and the volume fraction remains positive. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. More-over, a pressure relaxation procedure is used to fulfill the interface conditions. For validation, the results of sug-gested scheme are compared with those from the high resolution central upwind and HLLC schemes. The cen-tral upwind scheme is also applied for the first time to this model. The accuracy, efficiency and simplicity of th