EDGE, a Navier-Stokes solver for unstructured grids

This report describes the compressible Navier-Stokes solver EDGE for unstructured grids. The solver is based on an edge-based formulation for arbitrary elements and uses a node-centered finite-volume technique to solve the governing equations. Two spatial discretizations of the convection terms are described, compact discretizations of the thin-layer and fully viscous terms have been proposed and evaluated. The governing equations are integrated explicitly towards steady state with Runge-Kutta time integration. The convergence is accelerated with agglomeration multigrid and implicit residual smoothing. A validation is carried out in two and three dimensions for external flows. The validations focus on comparisons between EDGE and the cell centered solver EURANUS on structured grids. Also the effect of different types of elements are investigated. The results with the unstructured and structured approach compare well for all cases. The rate of convergence is comparable although higher CFL numbers can be used with the structured solver. The robustness of the unstructured solver is at least as good as with the structured solver. Two main differences are found. The first is that the decay of the maximum total pressure loss for subsonic Euler calculations is approximately second order accurate as the grid is refined for the node-centered scheme but only first order using the structured cell centered approach. The second difference concerns the flow over an airfoil at a low Reynolds number and no artificial dissipation. Here the rate of convergence is much slower with the unstructured approach. Small oscillations in the pressure can also be observed in the nose region.