An Implicit Flow Solver With Upwind Differencing For Three-Dimensional Hybrid Grids

摘要

An implicit point Gauss-Seidel relaxation scheme is described for solution of the unsteady Euler equations on unstructured hybrid grids in three dimensions. The use of generalized hybrid grids is motivated by the need for flexible discretization of complex configurations and subsequent solution of the unsteady Navier-Stokes equations. The solver uses a cell-centered finite-volume implementation with an unstructured face-based grid connectivity, which allows each cell to have an arbitrary number of bounding faces, and each face to have an arbitrary number of bounding nodes. The method to compute cell and face geometry metrics for arbitrary element types is described. The numerical flux is defined by a hybrid flux-vector splitting scheme, and the upwind states at each cell face are computed with a second-order accurate extrapolation of the flow solution. The cell-averaged flow gradient is computed with the Green-Gauss integral theorem, which requires the face-averaged solution that is constructed from the solution at the forming nodes. The solution at each node is reconstructed by a second-order accurate interpolation of cell-averaged data in all cells connected to the node. Flow solutions on generalized hybrid grids are presented for a NACA 0012 airfoil section in two dimensions, and a ONERA M6 wing configuration in three dimensions.