模式多重网格--一种新的加速收敛方法
Mode Multigrid - A novel convergence acceleration method
摘要：
提出了一种模式多重网格（MMG）方法，并将其应用于非结构网格上的定常流场计算。根据前几个时间步的解向量，采用动态模态分解（DMD）技术分析定常流场的收敛过程。与传统的多重网格方法不同，我们将流场解从物理空间投影到模态空间，并基于DMD分析截断所有高频模态，只保留一阶模态。物理空间中的实解可以通过模态空间的逆变换简单地得到。MMG方法巧妙地避免了计算网格粗化的复杂过程，不需要对物理空间的网格进行任何修改。因此，它可以很方便地应用于任何数值格式，只需对流场求解器进行很小的修改，也适用于非结构网格，易于并行计算。通过几个典型算例验证了该方法的有效性，结果表明，对于不同的网格类型、不同的空间离散精度和不同的时间推进格式，MMG都能显著减少迭代步数。该方法在保证计算精度的前提下，比原方法快3 ~ 6倍。
英文摘要：
This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of steady flow field according to the solution vectors from the previous time steps. Unlike the traditional multigrid method, we project the flowfield solutions from the physical space into the modal space, and truncate all the high-frequency modes but only the first-order mode are retained based on the DMD analysis. The real solutions in the physical space can be obtained simply by the inverse transformation from the modal space. The developed MMG method ingeniously avoids the complicated process of coarsening computational mesh, and does not need to make any change for the grid in physical space. Therefore, it is very convenient to be applied to any numerical schemes with just little change for the flow solver, which is also suitable for unstructured grids and easy for parallel computing. Several typical test cases have been used to verify the effectiveness of the proposed method, which demonstrates that the MMG can dramatically reduce the number of iterative steps for the different mesh types, different accuracy of spatial discretization and different time-marching schemes. The method is 3 to 6 times faster than the original method while ensuring the computational accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
