E. Blosch

Computational techniques for complex transport phenomena

1. Introduction 2. Numerical scheme for treating convection and pressure 3. Computational acceleration with parallel computing and multigrid methods 4. Multiblock methods 5. Two-equation turbulence models with non-equilibrium, rotation, and compressibility effects 6. Volume-averaged macroscopic transport equations 7. Practical applications References Index.

The role of mass conservation in pressure-based algorithms

Two numerical issues important to proper problem specification for pressure-based algorithms are investigated, including (1) well posedness of the pressure-correction equation, and (2) proper prescription of flow variables at open boundaries, particularly if inflow occurs. Lid-driven cavity flow and flow past a backward-facing step are used to help discuss the issues. It is shown that during each iteration, the explicit enforcement of global mass conservation is important even for the intermediate, nonconvergent flow field in order to maintain good convergence rates. This requirement stems from the fact that the pressure distribution is an outcome of the continuity equation. Furthermore, it seems that the global continuity constraint is often sufficient for the numerical problem for a flow with an open boundary to be well posed, regardless of whether or not inflow occurs at that boundary. Thus, in the pressure-based algorithm with a staggered grid the downstream boundary can, if necessary, pass through a ...

SEQUENTIAL PRESSURE-BASED NAVIER-STOKES ALGORITHMS ON SIMD COMPUTERS: COMPUTATIONAL ISSUES

Abstract Computational issues relevant to parallel efficiency and algorithm scalability are explored on three massively parallel, single-instruction-stream s multiple-data-stream lSIMDr computers, Thinking Machines’ CM-2 and CMS, and MasPars 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...