In this article, the space-time conservation element and solution element scheme is extended to simulate the unsteady compressible two-phase flow in pipes. The model is non-conservative and the governing equations consist of three equations, namely, two mass conservation equations for each phase and one mixture-momentum equation. In the third equation, the non-conservative source term appears, which describes the sum of gravitational and frictional forces. The presence of source term and two mass conservation equations in considered model offers difficulties in developing the accurate and robust numerical techniques. The suggested space-time conservation element and solution element numerical scheme resolves the volume-contact discontinuities efficiently. Furthermore, the modified central upwind scheme is also extended to solve the same two-phase flow model. The number of test problems is considered, and the results obtained by space-time conservation element and solution element scheme are compared with the solutions of modified central upwind scheme. The numerical results show better performance of the space-time conservation element and solution element method as compare to the modified central upwind scheme.
Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids