High order finite volume weighted essentially non-oscillatory scheme for solving the isentropic two-phase flow model

Abstract

This article presents the fifth-order weighted essentially non-oscillatory numerical method for solving a five-equation two-pressure non-conservative model of isentropic two-phase flow. The presence of non-conservative terms, shock waves and contact discontinuities offers more challenging tasks for developing the high order robust numerical methods. The proposed numerical scheme suppresses the unwanted oscillations near the steep gradients and resolves the contact discontinuities in an efficient way. Further, different test problems are taken to validate the efficiency of the proposed numerical scheme. Moreover, the improved central upwind scheme (CUP) is extended to solve the same model for checking the accuracy of the proposed numerical method. The numerical solutions obtained by the suggested scheme are compared with the solution profiles obtained from modified central upwind scheme.

Keywords

• Two-phase model
• WENO scheme
• Non-conservative terms
• Interfacial pressure
• Interfacial velocity
• Shock wave