Efficient Implicit Non-linear LU-SGS Approach for Viscous Flow Computation Using High-Order Spectral Difference Method

Abstract

An implicit non-linear lower-upper symmetric Gauss-Seidel (LU-SGS) solution algorithm has been developed for a high-order spectral difference Navier-Stokes solver on unstructured hexahedral grids. The non-linear LU-SGS solver is preconditioned by the block element matrix, and the system of equations is then solved with a LU decomposition approach. The large sparse Jacobian matrix is computed numerically, resulting in extremely simple operations for arbitrarily complex residual operators. Several viscous test cases were performed to evaluate the performance. The implicit solver has shown speedup of 1 to 2 orders of magnitude over the multi-stage Runge-Kutta time integration scheme.