A high-order diffuse-interface method with TENO-THINC scheme for compressible multiphase flows

High-fidelity numerical simulation of compressible multi -phase flows is of great challenge due to its competing requirements for resolving complex flow structures with low dissipation and capturing moving interfaces as well as other discontinuities sharply. Recently, a novel hybrid scheme, combining the standard targeted essentially non -oscillatory (TENO) scheme with Tangent of Hyperbola for INterface Capturing (THINC) scheme as two building blocks for smooth and non -smooth regions respectively and thus named as TENO-THINC, has been proposed and shows great potential for resolving complex single-phase fluids. In this work, a high -order finite -volume method, based on the TENO-THINC scheme for spatial reconstruction and the Harten-Lax-van Leer contact (HLLC) approximate Riemann solver for flux evaluation, is developed for simulating compressible multi -phase flows with a reduced five -equation formulation of the diffuse -interface model. The TENO-THINC scheme deploys the THINC reconstruction to resolve the physical discontinuities as well as the material interfaces within a few cells, and is desired to resolve the interface evolution more reliably in multi -phase flow simulations. Several algorithms have been implemented and elaborated for ensuring the numerical robustness of extreme simulations with high density and pressure ratios. Numerical results of the 1D and 2D challenging benchmark tests show that the TENO-THINC scheme is more robust than the standard TENO scheme and less dissipative than both the TENO and WENO-JS schemes. This property is essential for the long-term simulations of compressible multi -phase flows.