Edge-Based Viscous Method for Node-Centered Finite-Volume Formulation on Tetrahedra

Abstract

This paper presents a novel, efficient, edge-based viscous (EBV) discretization for finite-volume, node-centered formulations on tetrahedral grids. This new method is implemented in a practical, unstructured-grid Reynolds-averaged Navier–Stokes solver and applied to viscous-kernel computations that include evaluations of mean flow viscous fluxes, turbulence-model diffusion terms, and the corresponding Jacobian contributions. The EBV method uses an efficient loop over edges and features a compact discretization stencil based on nearest neighbors. This study verifies the EBV method by comparing its accuracy and iterative convergence with those of a well-established method based on a cell-based approach to discretization of viscous fluxes. Multifold efficiency gains for all viscous-kernel computations on tetrahedral grids are reported, leading to a significant reduction of the overall time to solution.