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给出了一种适用于混合网格的并行无矩阵GMRES+LU-SGS隐式时间格式。首先采用LU-SGS方法迭代若干步以获得一个合适的初场,然后切换到GMRES方法在每一时间步内近似求解,并将LU-SGS方法作为其预处理器。为加速收敛,将CFL数随着残差的降低逐步放大;为减少存储量和计算量,通量Jacobian采用无矩阵处理。在保证与串行执行一致的前提下,采用基于共享内存的OpenMP方法实现了并行计算,并通过对网格的分组避免了内存争夺。算例验证表明,方法极大地提高了计算收敛效率,并行结果与串行结果完全一致,计算结果与实验结果吻合较好。
A parallel matrixless GMRES + LU-SGS implicit time format for hybrid grid is given. Firstly, LU-SGS method is used to iterate a number of steps to obtain a suitable initial field, then switch to the GMRES method to approximate the solution in each time step, and use the LU-SGS method as its preprocessor. In order to speed up the convergence, the CFL number is gradually enlarged as the residual decreases. In order to reduce the amount of storage and calculation, the flux Jacobian uses matrix-free processing. Under the premise of guaranteeing that it is consistent with serial implementation, OpenMP method based on shared memory realizes parallel computing and avoids memory contention by grouping the grids. The example verification shows that the method greatly improves the efficiency of calculation convergence. The parallel result is in good agreement with the serial result, and the calculated result agrees well with the experimental result.