A high-robustness hybrid scheme of finite-difference WENO-THINC for compressible multicomponent flow scheme on general curvilinear grids

Abstract

In this study, a high-robustness hybrid scheme of weighted essentially non-oscillatory (WENO) scheme with a modified tangent of hyperbola for interface capturing (THINC) algorithm is developed for compressible multicomponent flow on general curvilinear grids. Numerical errors induced by mesh deformation bring loss of numerical accuracy and simulation instability, resulting in inaccurate results such as interface distortion, numerical oscillations or even simulation failure. To address this issue, the WENO scheme combined with an improved THINC strategy is designed to alleviate these errors and maintain the high resolution of interfaces. A modified THINC algorithm is developed for the non-uniform grids, in which the steepness parameter is scaled adaptively according to varying grid spacings. This approach is capable of reducing numerical dissipations for interface reconstruction. The overestimated quasi-conservative WENO formulation are employed to hold the equilibriums of velocity, pressure, and temperature at the material interface. Numerical validations are tested on non-uniform grids with various randomness amplitudes to verify the effectiveness in one- and two-dimensional benchmark problems showing the better performances in shock- and interface-capturing capabilities.