Convergence Assessment of General Fluid Equations on Unstructured Hybrid Grids

A general finite volume formulation for arbitrary fluids on generalized grids is presented and solved by implicit methods. Primary focus is on a line GaussSeidel method modified for unstructured grids, and a GMRES method. The effects of grid aspect ratio and control volume shape on convergence rates are addressed parametrically by means of simple problems. An effort is made to define an appropriate Courant number that allows various problems and various flow regimes to converge at near-optimum speeds for a single CFL value. Results show that both the LGS and GMRES methods give excellent aspect-ratio-independent convergence for rectangles, and good convergence for triangles. Results for hexahedrons are likewise good while for tetrahedrons or prisms much wider variations in convergence rates remain. Gauss-Seidel and LU methods are very effective for isotropic grids but slow dramatically as grid aspect ratios are increased. Representative applications of the modified LGS method to flows past airfoils on hybrid grids show excellent convergence for high and low Reynolds numbers and for subsonic and transonic Mach numbers.