An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids (Communications in Computational Physics, 2020)
An efficient implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solutionapproach has been applied to a high order spectral volume (SV) method for unstructuredtetrahedral grids. The LU-SGS solver is preconditioned by the block elementmatrix, and the system of equations is then solved with a LU decomposition.The compact feature of SV reconstruction facilitates the efficient solution algorithmeven for high order discretizations. The developed implicit solver has shown morethan an order of magnitude of speed-up relative to the Runge-Kutta explicit schemefor typical inviscid and viscous problems. A convergence to a high order solution forhigh Reynolds number transonic flow over a 3D wing with a one equation turbulencemodel is also indicated.