Numerical solution of compressible, isothermal two-fluid models using path-conservative central schemes

Two-fluid models are the most accurate and complex models for analysis of two-phase flows. There are two different two-fluid models for analyzing compressible isothermal two-phase flows which are Single Pressure Model (SPM) and Two-Pressure Model (TPM). In spite of capabilities of these models in capturing two-phase flow behavior، it is not possible to express them in conservative form due to existence of non-conservative term in momentum equation of phases. Therefore، the classical Rankine-Hugoniot condition across discontinuities in the flow filed is not applicable for these equations and there would be difficulty in using classical numerical methods for solving these equations. In this paper a new path-conservative method is used to overcome this difficulty. In this method، one can apply general Rankine-Hugoniot condition along a path connecting left and right states of the discontinuity. After expressing path-conservative form of the employed central numerical methods which are Lax-Fridriches، Lax-Wendroff and Rusanove، water faucet and large relative velocity shock tube problems are solved by using these schemes. Grid independence was achieved using different grid sizes. For water faucet problem، comparison of numerical results with analytical solution show good agreement and for shock tube problem، the results indicate that this method is highly capable in capturing discontinuities in two-phase flow.