Please use this identifier to cite or link to this item:
https://hdl.handle.net/11681/13343| Title: | Development of an efficient solication scheme for incompressible steady-state flow |
| Authors: | Holland, Jeffery P. |
| Keywords: | Convergence acceleration Navier-Stokes equations Finite-volume scheme Predictor-corrector scheme Incompressible flow Pseudocompressibility Multigrid Navier-Stokes equations Hydrodynamics |
| Publisher: | Hydraulics Laboratory (U.S.) Engineer Research and Development Center (U.S.) |
| Series/Report no.: | Technical report (U.S. Army Engineer Waterways Experiment Station) ; HL-89-8. |
| Description: | Technical Report Abstract: This study advances the understanding of the numerical simulation of steady-state, incompressible flows through development of a new solution methodology for the two-dimensional Navier-Stokes equations. The study presents details of a numerical scheme formulated specifically to simulate flows generally observed in the approaches to hydraulic structures. An explicit predictor-corrector finite volume relaxation scheme is coupled with a pseudocompressibility methodology to integrate the governing equations of motion and continuity. The use of the pseudocompressibility concept negates the need for the solution of a Poisson equation relating the pressure and flux fields. Results from the simulation of four model case studies show the efficacy of the relaxation scheme. To accelerate the convergence of the basic relaxation scheme, a multigrid algorithm is coupled with the predictor-corrector. The multigrid approach is patterned after the works of Brandt and Jameson and Yoon. Results from additional simulation of the four model case studies conclusively show the validity and attractiveness of employing the multigrid approach in the simulation of incompressible, steady-state flows. The flow fields numerically generated through inclusion of the multigrid algorithm are just as accurate as those computed with the basic relaxation scheme alone. In addition, the model test case results obtained with the multigrid algorithm are generally from 3 to 12 times more efficient in reaching a predefined convergence tolerance than their relaxation scheme-only counterparts based on computer resource usage. The inclusion of the multigrid algorithm requires more computational overhead than the basic relaxation scheme computations, however, porducing up to a nine-fold increase in the time per iteration compared to these latter computations. This computational overhead is easily compensated for by the reduction in the number of iterations required to reach convergence with the multigrid algorithm included. The optimal multigrid setup was that which utilizes the maximum number of total grids allowable given the resolution on the finest grid. In addition, convergence is most faithfully accelerated by the use of one or two relaxation sweeps on the finest grid in concert with the use of one relaxation sweep on each of the coarser grids employed. |
| Rights: | Approved for public release; distribution is unlimited. |
| URI: | http://hdl.handle.net/11681/13343 |
| Appears in Collections: | Technical Report |
