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Domain decomposition methods for fluid dynamics. (English) Zbl 0861.76070
Sequeira, A. (ed.), Navier-Stokes equations and related nonlinear problems. Proceedings of the 3rd international conference, held May 21-27, 1994 in Funchal, Madeira, Portugal. Funchal: Plenum Press. 367-376 (1995).
The authors show that the solution of the nonlinear, imcompressible, two-dimensional Navier-Stokes equations in vorticity-streamfunction formulation can be reduced to the solutions of linear equations, namely to the successive solutions of symmetric and nonsymmetric (convection-diffusion) linear systems. In particular, the numerical solution on parallel computers MIMD (Multiple Instruction Multiple Data) of the linear systems arising from the discretization of the convection-diffusion equation is considered. The authors point out that domain decomposition methods seem to be natural and promising approach. The discretization of the convection-diffusion equation, however, leads to nonsymmetric linear systems of equations. A method based on the use of artificial boundary conditions (ABC) is presented. First, the problem is reformulated as a problem whose unknowns are functions of the boundaries of the subdomains. Next, as interface conditions are taken exact ABC. It is demonstrated that GMRES and BICGSTAB algorithms converge in a number of steps equal to the number of subdomains minus one. Since the exact ABC are difficult to use, they are approximated by partial differential operators. Numerical results for the convection-diffusion equation are presented.
For the entire collection see [Zbl 0833.00032].
Reviewer: J.Siekmann (Essen)

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids