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Computational Science, Engineering & Technology Series
ISSN 1759-3158
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

Full Bibliographic Reference for this chapter
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", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 17, pp 300-314, 1999. doi:10.4203/csets.2.17
The test problem used is the steady 2-D incompressiblelaminar flow in a square lid-driven cavity. We will consider the linear system generated by a coupled discretization and linearization method for the Navier-Stokes 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 non-null 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.

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