Fast, block lower-upper symmetric Gauss-Seidel scheme for arbitrary grids

A block implicit lower-upper symmetric Gauss-Seidel (LU-SGS) approximate factorization scheme is developed and implemented for unstructured grids of arbitrary topology including viscous adaptive Cartesian grids. CPU times and memory requirements for the block LU-SGS (BLU-SGS), the original LU-SGS, and a fully implicit scheme (FIS) with a preconditioned conjugate gradient squared solver for several representative test examples are compared. Computational results showed that the block LU-SGS scheme requires about 20-30 % more memory than the original LU-SGS but converges many times faster. The BLU-SGS scheme has a convergence rate competitive to and in many cases faster than the FIS while requiring much las memory.