Sequential pressure-based Navier-Stokes algorithms on SIMD computers: Computational issues

Computational issues relevant to parallel efficiency and algorithm scalability are explored on three massively parallel, single-instruction-stream / multiple-data-stream (SIMD) computers, Thinking Machines’ CM-2 and CMS, and MasPar's MP-l, for a two-dimensional semiimplicit sequential pressure-based Navier-Stokes algorithm, by increasing the problem size up to 10₆ points on a fixed number of processors. On the CMS and MP-I, parallel efficiencies approaching 0.85 are obtained, using a point-Jacobi iterative solver. To obtain peak efficiency, however, the CM-5 requires larger problems than the MP-I, by a factor of 64. To compare with point-Jacobi, a line-Jacobi solver that uses parallel cyclic reduction has also been implemented, and, on the CM-2, the performance in Mflops is consistent with reported results. A uniform approach for boundary coefficient computations is recommended—with separate treatment of interior and boundary control volumes, the run time increases substantially and shows a strong square-root dependency over the entire range of problem sizes on the CM-2. By varying the mesh aspect ratio at a given problem size, the effect of Ike data layout is revealed; the run time can be affected by as much as 25% in going from square to high-aspect-ratio virtual subgrids. With a point-iterative solver, sequential pressure-based algorithms are linearly scalable, and can be efficiently implemented on those data-parallel computers such as the MP-I and CMS that provide relatively fast nearest-neighbor communications, compared to the speed of computation.