An implicit spectral difference Navier-Stokes solver for unstructured hexahedral grids

A spectral difference (SD) solver using quadrilateral and hexahedral grids for the Navier- Stokes equations is presented. Three different approaches for the discretization of the diffusive terms with the SD method are tested and compared. These approaches are the local SD approach, the second approach of Bassi and Rebay and the interior penalty ap- proach. Furthermore, two implicit methods to solve the nonlinear algebraic systems arising from SD discretizations have been implemented. The first is a Newton-Raphson method in combination with a generalized minimum residual algorithm to invert the associated linear algebraic systems. The second method is the (nonlinear) lower-upper symmetric Gauss-Seidel method. These two methods are used to solve the 2D laminar flow over a cylinder, and the 3D laminar flow through a pipe with a 90° bend, using the three different approaches for the diffusive terms. The obtained results are compared and the performance of the algebraic solvers in terms of CPU-time and memory is evaluated.