The incompressible Navier-Stokes equations are solved in a channel, using a Discontinuous Galerkin method over staggered grids. The resulting linear systems are studied both in terms of the structure and in terms of the spectral features of the related coefficient matrices. In fact, the resulting matrices are of block type, each block showing Toeplitz-like, band, and tensor structure at the same time. Using this rich matrix-theoretic information and the Toeplitz, Generalized Locally Toeplitz technology, a quite complete spectral analysis is presented, with the target of designing and analyzing fast iterative solvers for the associated large linear systems. Quite promising numerical results are presented, commented, and critically discussed for elongated two- and three-dimensional geometries.
翻译:压缩的纳维-斯托克方程式在一个频道中解答,在交错格格上采用不连续的加列金法,对由此形成的线性系统进行结构和相关系数矩阵光谱特征的研究,结果的矩阵是块型的,每个区块显示类似托普利茨、波段和高压结构,同时使用这种丰富的矩阵理论信息以及托普利茨通用本地化托普利茨技术,提供了相当完整的光谱分析,目标是为相关的大型线性系统设计和分析快速迭代解码器,为长长的二维和三维的地形提供了很有希望的数字结果,并作了评论和严格讨论。