Edge-Based Viscous Method for Mixed-Element Node-Centered Finite-Volume Solvers

A novel, efficient, edge-based viscous (EBV) discretization method has been recently developed and implemented in a practical, unstructured-grid, node-centered, finite-volume flow solver. The EBV method is applied to viscous-kernel computations that include evaluations of mean-flow viscous fluxes, turbulence-model and chemistry-model diffusion terms, and the corresponding Jacobian contributions. Initially, the EBV method had been implemented for tetrahedral grids and demonstrated multifold acceleration of all viscous-kernel computations. This paper presents an extension of the EBV method for mixed-element grids. In addition to the primal edges of a given mixed-element grid, virtual edges are introduced to connect cell nodes that are not connected by a primal edge. The EBV method uses an efficient loop over all (primal and virtual) edges and features a compact discretization stencil based on the nearest neighbors. This study verifies the EBV method and assesses its efficiency on mixed-element grids by comparing the EBV solution accuracy and iterative convergence with those of well-established solutions obtained using a cell-based viscous (CBV) discretization method. The EBV solver's memory footprint is optimized and often smaller than the memory footprint of the CBV solver. An EBV implementation of a nonlinear extension of the Spalart-Allmaras turbulence model, SA-neg-QCR2000, is also presented and verified. The SA-neg-QCR2000 model is used for simulating turbulent corner flows. Multifold speedup is demonstrated for all viscous-kernel computations, resulting in significant reduction of the time to solutions for several benchmark mixed-element-grid computations, including simulations of subsonic flows around a hemisphere-cylinder configuration and a NASA juncture-flow model, a supersonic flow through a long square duct, and a hypersonic, chemically reacting flow around a blunt body.