A limiter free adaptive THINC-BVD scheme with AUSMV numerical flux for solving the drift flux model

In this article, adaptive THINC-BVD (Tangent of Hyperbola for Interface Capturing)-(Boundary Variations Diminishing) numerical scheme with AUSMV (Advection Upstream Splitting Method based on flux vector splitting) numerical flux is developed for solving the two-phase drift flux model. The drift flux model is considered for analyzing the transient two-phase flow phenomenon in the pipe-lines. This model comprises the two mass conservation equations, one for each phase, and a momentum equation for the mixture of both phases. The mixture momentum equation contains the non-conservative terms. Further, for computation purpose, thermodynamic and hydrodynamic sub-models are considered to close the drift flux model. These non-conservative terms and sub-models offer difficulties in designing the efficient numerical schemes. In the considered adaptive numerical scheme, THINC functions are used for the spatial reconstruction and BVD algorithm is used to minimize the large variations of reconstructed variables at the cell-interfaces. Thus, the developed numerical scheme has great potential to resolve the sharp discontinuities in an efficient and simple way. Various benchmark test problems are considered to verify the robustness of developed adaptive numerical scheme. •Develop THINC-BVD numerical scheme with AUSMV numerical flux for unsteady two-phase flow in horizontal pipe-lines.•The proposed numerical scheme has great potential to resolve the high gradients as compared to the fifth order WENO numerical scheme at the same computational time.•The developed numerical technique captures the peaks of pressure waves.•The accuracy of proposed numerical technique is verified by solving the various test problems.•The solution profiles are compared to those obtained with the improved central upwind, AUSMV and WENO numerical schemes.