Enhancing Accuracy in Mixed-Element Grids and Convergence on Skewed Grids for the Two-Dimensional Edge-Based Compressible Navier-Stokes Solver

In this paper, we apply a recently proposed flux correction for finite-volume discretizations to an edge-based compressible Navier-Stokes solver. Through numerical experiments, we demonstrate that applying this correction solely to the inviscid terms of the equations results in second-order convergence of the discretization error, without any modification of the viscous terms. Second-order accuracy is achieved on arbitrary mixed-element grids and for a wide range of Reynolds numbers including both convection- and viscous-dominated flows. Second-order accuracy is preserved also for an arbitrary centroid definition, which is known to destroy secondorder accuracy of the edge-based solver, and the face-area-weighted centroid can result in faster time-to-solution for skewed triangular grids. Results show that the proposed scheme yields a truly grid transparent discretization that can be used to enhance accuracy on mixed-element grids and accelerate convergence on stretched triangular meshes.