High order multi-resolution WENO scheme with AUSMV numerical flux for solving the two-phase flows

This article presents the development of a fifth-order multi-resolution finite volume weighted essentially non-oscillatory (WENO) scheme combined with the advection upstream splitting method based on flux vector splitting (AUSMV) numerical flux for analyzing two-phase flow in both horizontal and vertical pipelines. The drift flux flow model comprises of two separate mass conservation equations for each phase for liquid and gas and one momentum equation for mixture and submodels for thermodynamics and hydrodynamics. The two mass conservation equations describe the behavior of each phase in the flow. The mixture-momentum equation takes into account the frictional and gravitational forces acting on the mixture of both phases. The thermodynamic and hydrodynamic submodels provide additional information to fully describe the flow and close the drift flux model. In the presence of these source terms and submodels, it is a challenging task to develop a high order efficient and accurate numerical schemes. The proposed numerical technique captures the peaks of pressure wave, suppresses the erroneous oscillations at the transition zones and resolves the discontinuities more efficiently and accurately. The accuracy of proposed numerical technique is verified by solving the various test problems. Furthermore, the solution obtained by developed numerical technique are compared to those attained with the high-resolution improved CUP and simple finite volume WENO numerical schemes.