Numerical simulations of compressible multicomponent and multiphase flow using a high-order targeted ENO (TENO) finite-volume method

High-order numerical simulations of compressible multicomponent and multiphase flows are challenging due to the need to resolve both complex flow features and sharp gradients associated with material interfaces or shocks with minimal spurious oscillations. Recently, in the context of the WENO family of schemes, increasing the ENO property and incorporating improved convergence properties near local extrema points, has resulted in the targeted ENO or TENO scheme. In this study, a robust high-order finite-volume method based on the TENO scheme is implemented and tested for simulating multicomponent and multiphase compressible flows. A fifth-order spatial reconstruction is combined with a high-resolution modified HLLC Riemann solver, adjusted for the six-equation formulation of the diffuse interface model, and a third-order TVD Runge-Kutta explicit time-stepping scheme. Multidimensional extension is handled utilizing Gauss-Legendre quadrature points to evaluate both the flux and gas void fraction inter-cell terms. Several challenging 1D and 2D test cases are performed and compared to previously published experimental data and numerical simulations where available. A parametric study of the user-defined threshold parameter in the TENO algorithm is also studied and the TENO scheme is found to be more robust and less dissipative than both the WENO-Z and WENO-JS schemes.