A low-dissipation WENO-THINC scheme for freestream and vortex preservation on general curvilinear grids

In this paper, we present a modified tangent of hyperbola for interface capturing (THINC) scheme for freestream and vortex preservation on the general curvilinear grids, in which the symmetric conservative metric method is employed to eliminate the geometrical errors in the discretization of Jacobian and the metrics. As the original THINC with a fixed jump steepness may lose accuracy and result in instability problem on non-uniform grids, a new algorithm is introduced to reduce the numerical dissipation, in which the jump steepness is scaled adaptively according to varying mesh intervals. Numerical tests show the new THINC scheme can hold freestream and vortex preservation and is capable of resolving discontinuities and small-scale smooth flow structures with less dissipation on general curvilinear grids, compared with the original THINC. By using the boundary variation diminishing (BVD) principle, the modified THINC is implemented in combination with a finite-difference weighted essentially non-oscillatory (WENO) scheme. Comprehensive numerical validations are performed to evaluate the performance of the improved THINC and WENO combined with the modified THINC in the framework of both the FDM and FVM, with twisting and even randomly spaced curvilinear meshes. Numerical results of the double Mach reflection also demonstrate the improved THINC can alleviate non-physical oscillations with less numerical dissipation.