Computational & Technology Resources
an online resource for computational,
engineering & technology publications 

Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 2
PARALLEL AND DISTRIBUTED PROCESSING FOR COMPUTATIONAL MECHANICS: SYSTEMS AND TOOLS Edited by: B.H.V. Topping
Chapter 17
Parallelisation of an Implicit Algorithm for Fluid Flow Problems F.D. d'Almeida and P.B. Vasconcelos
Faculty of Engineering, University of Porto, Porto, Portugal F.D. d'Almeida, P.B. Vasconcelos, "Parallelisation of an Implicit Algorithm for Fluid Flow Problems", in B.H.V. Topping, (Editor), "Parallel and Distributed Processing for Computational Mechanics: Systems and Tools", SaxeCoburg Publications, Stirlingshire, UK, Chapter 17, pp 300314, 1999. doi:10.4203/csets.2.17
Abstract
The test problem used is the steady 2D incompressiblelaminar flow
in a square liddriven cavity. We will consider the linear system generated by a
coupled discretization and linearization method for the NavierStokes equations.
This method consists of a discretization of the momentum equations to obtain the velocities at the faces of a finite volume, in terms of the values of these variables at the grid points followed by the integration of the momentum and continuity equations in the finite volumes. This integration leads to equations where the values of the variables at the cell faces are to be replaced by the expressions obtained at the previous stage. The linear system to be solved at each nonlinear iteration connects values of velocities and pressure at each grid point in each equation. The coefficient matrix is large, nonsymmetric, sparse, with nonnull entries on the diagonal. The characteristics of these linear systems indicate the use of nonstationary iterative methods, for instance preconditioned GMRES, for their solution. The strategy used to parallelize this method was nonoverlapping domain decomposition. The linear system to be solved at each outer iteration is then equivalent to the solution, on the interfaces separating subdomains, of the Schur complement reduced system followed by the update of the solution in the subdomains. Numerical tests will be reported showing the number of outer iterations and elapsed times of this code on a Transputer based machine, compared to the corresponding results on a cluster of workstations. purchase the fulltext of this chapter (price £20)
go to the previous chapter 
