An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids

Abstract

An efficient implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solu- tion approach has been applied to a high order spectral volume (SV) method for un- structured tetrahedral grids. The LU-SGS solver is preconditioned by the block ele- ment matrix, and the system of equations is then solved with a LU decomposition. The compact feature of SV reconstruction facilitates the efficient solution algorithm even for high order discretizations. The developed implicit solver has shown more than an order of magnitude of speed-up relative to the Runge-Kutta explicit scheme for typical inviscid and viscous problems. A convergence to a high order solution for high Reynolds number transonic flow over a 3D wing with a one equation turbulence model is also indicated. AMS subject classifications: 65M70, 76M12, 76M22