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

“…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 [3,5,11,13,17,18,20,22,25,27,28,31,32], only Demirdžić 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. As mentioned earlier, Demirdžić et al [5] have presented solutions for skewed cavity for Reynolds number of 100 and 1000 for skewed angles of α = 45 • and α = 30 • .…”

“…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 α = 30 • and α = 45 • , and also the maximum number of grids used in these studies is 320 × 320.…”

Domain decomposition for the incompressible Navier-Stokes equations: solving subdomain problems accurately and inaccurately

“…where A 11 and A 22 represent the subdomain discretization matrices and A 12 and A 21 represent the coupling between subdomains. Unaccelerated domain decomposition iteration for ( 8) is of the following form v m+1 = (I N 1 A)v m + N 1 f; (10) with N 1 an approximation to the inverse of the block diagonal or block lower-triangular matrix of A. The matrix N is called the block Jacobi or Gauss-Seidel matrix of A, depending on the method used.…”

“…Similar to Schwarz domain decomposition, in each iteration, subdomain problems are solved using values from neighboring blocks. For instance, formula (10) interpreted for domain 1 becomes…”

Graphics hardware acceleration for rotorcraft simulations

“…The SIMPLER algorithm consists of the following steps: Incompressible flow solvers have been created using this method in Brakkee et al in [18,19,30].…”