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

Abstract

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 (). 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.