适用于混合网格的改进雅可比迭代法及其应用

Improved Jacobi iterative method for hybrid grid and its application

LU-SGS因有较高的鲁棒性和小的内存需求而得到广泛应用,然而用于混合网格计算前需要进行网格排序和分组来实现算法并行;此外,LU-SGS格式收敛效率不高。针对这些缺点,本文提出了一种改进的适用于复杂混合网格的雅可比迭代方法,无需网格排序和分组就可实现算法的并行化,且有较快的收敛速度。该方法编程实现简单,易于采用Open MP实现并行。算例研究表明,相比于LU-SGS格式,在各来流条件下,本文提出的方法收敛速度更快,鲁棒性好,并行和串行结果一致,且内存需求增加很少。

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 Open MP 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.