A revised WENO-THINC scheme for the general structured mesh and applications in the direct numerical simulation of compressible turbulent flows

The Tangent of Hyperbola for INterface Capturing (THINC) scheme allows a jump-like reconstruction and brings about a significant improvement in resolving the discontinuous part of the numerical solutions. However, it is found that the original THINC scheme loses accuracy when working on the stretched, curvilinear or highly-skewed grid. In this study, we propose a simple strategy to determine the jump thickness parameter in the THINC function, so as to effectively suppress the unphysical oscillation. A Boundary Variation Diminishing (BVD) guideline is introduced to make options between the Weighted Essentially Non-Oscillatory (WENO) scheme and the modified THINC scheme, thus both the smooth and discontinuous solutions can be reconstructed properly avoiding distortion of grids. Numerical validations indicate that the improved WENO-THINC-BVD approach maintains high resolution and is more robust on various types of non-uniform meshes. The present method is further extended to validate the low-dissipation property in resolving higher wave numbers portions by simulating an isotropic turbulence decay problem. Finally, we perform the direct numerical simulation (DNS) of a spatially evolving adiabatic flat plate boundary-layer flow problem at a supersonic Mach number (Ma=2.25$$ Ma=2.25 $$). Numerical results show the predicted mean flow variables and the normalized shear stress agree well with the experimental data, significant improvements are found in the resolution of the small-scale vortices, especially in the transition process.