Cartesian mesh with a novel hybrid WENO/meshless method for turbulent flow calculations

Abstract

In this paper we explore a new hybrid method for the near-wall treatment of turbulent flow computation with Cartesian mesh. Cloud of points are generated to resolve the boundary layer and they are generated along wall-normal directions. Special attention is paid at the treatment of singular point for the use of current method for complex geometry. Multiple marching directions are defined for enough resolution and smooth transition between near-wall and off-wall solvers. These points demonstrate one dimensional structure in the wall-normal direction and it offers the opportunity of improved accuracy. By exploring this property, a hybrid methodology combines high order scheme in the wall-normal direction and meshless method in the streamwise direction is proposed. Also a hybrid LU-SGS/line-implicit time integration method is developed based on this property. The use of high order scheme for the wall-normal flow derivative significantly improves the overall accuracy, especially in the area with curved solid surface. The current hybrid method is verified using Method of Manufactured Solution (MMS) and a series of turbulent test cases. Results indicate good agreement with available experimental values and improved predictions and robustness compared to the meshless method.