Schwarz domain decomposition for the incompressible Navier-Stokes equations in general co-ordinates

Numerical solutions of 2‐D steady incompressible flow in a driven skewed cavity

“…The skewed cavity problem is a perfect test case for body fitted non-orthogonal grids and yet it is as simple as the cavity flow in terms of programming point of view. Later Oosterlee et al [17], Louaked et al [13], Roychowdhury et al [20], Xu and Zhang [31], Wang and Komori [28], Xu and Zhang [32], Tucker and Pan [27], Brakkee et al [3], Pacheco and Peck [18], Teigland and Eliassen [25], Lai and Yan [11] and Shklyar and Arbel [22] have solved the same benchmark problem. In all these studies, the solution of the driven skewed cavity flow is presented for Reynolds numbers of 100 and 1000 for only two different skew angles which are 30 …”

“…In order to do this we compare our results with the results found in the literature. At this point, we would like to note that in the literature among the studies that have solved the skewed cavity flow ( [5], [17], [13], [20], [31], [28], [32], [27], [3], [18], [25], [11] and [22]), only Demirdžiü et al [5], Oosterlee et al [17], Shklyar and Arbel [22] and Louaked et al [13] have presented tabulated results therefore we will mainly compare our results with those studies.…”

An advanced multi-block method for the multiresolution modelling of EFG silicon tube growth

“…Since the contributions from nodes in the neighbouring blocks are not included in the iteration matrix, the number of iterations required will be larger than that in a single block grid system. In fact, this is called block Gauss-Seidel preconditioner in the domain decomposition technique (Brakkee et al 2000). The degradation of the convergence rate of the linear equation solvers is called numerical inefficiency.…”