Parallel finite element computation of unsteady incompressible flows

✍ Scribed by Tamer Wasfy; Alan C. West; Vijay Modi

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 472 KB
• Volume: 26
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(19980115)26:1<17::aid-fld619>3.0.co;2-g

✦ Synopsis

A parallel semi-explicit iterative ®nite element computational procedure for modelling unsteady incompressible ¯uid ¯ows is presented. During the procedure, element ¯ux vectors are calculated in parallel and then assembled into global ¯ux vectors. Equilibrium iterations which introduce some `local implicitness' are performed at each time step. The number of equilibrium iterations is governed by an implicitness parameter. The present technique retains the advantages of purely explicit schemes, namely (i) the parallel speed-up is equal to the number of parallel processors if the small communication overhead associated with purely explicit schemes is ignored and (ii) the computation time as well as the core memory required is linearly proportional to the number of elements. The incompressibility condition is imposed by using the arti®cial compressibility technique. A pressureaveraging technique which allows the use of equal-order interpolations for both velocity and pressure, this simplifying the formulation, is employed. Using a standard Galerkin approximation, three benchmark steady and unsteady problems are solved to demonstrate the accuracy of the procedure. In all calculations the Reynolds number is less than 500. At these Reynolds numbers it was found that the physical dissipation is suf®cient to stabilize the convective term with no need for additional upwind-type dissipation.