Improved Jacobi iterative method for hybrid grid and its application

LU-SGS scheme is widely used today because of its robustness and cheap memory cost. However, the original LU-SGS shows less competitive convergence rate; in order to apply paralleled codes on hybrid unstructured grid, the grid reordering and regrouping procedure must be carried out beforehand. In this paper, an improved implicit method suitable for complex hybrid gird is developed to achieve fast convergence rate and to parallelize the algorithm without grid reordering and regrouping procedure. This method is simple for coding and easy to use OpenMP for code parallelization. The numerical results of Euler and viscous flows show that the method has a reliable performance, and it is able to achieve a significant efficiency improvement over implicit counterparts such as LU-SGS scheme with less requirement of extra memory, and parallel computation produce exactly the same result as serial case.