Efficient solution of Euler/N-S equations on unstructured grids

The implicit time integration method has been investigated to be an efficient approach for solving Euler/Navier-Stokes (N-S) equations. The resulting linear equations are typically large, sparse, nonsymmetric, and ill-conditioned. In general, the linear equations are approximately solved through LU-SGS, symmetric Gauss-Seidel and GMRES algorithms, etc. Compared to the structured grid, the order of unstructured grid is irregular, which significantly affects the computational efficiency. In the traditional efficiency analysis, the effect of spatial efficiency has been hardly considered. The different calculations and comparisons were presented in the paper. If the memory requirement is accomplished, GMRES algorithm is efficient. But the calculation of SA turbulence model in N-S equations affects the rate of the convergence. If the spatial discretization is efficient, the symmetric Gauss-Seidel with inner iterations is performed well. It is a better choice for the large-scale calculations, especially for viscous flow.