Domain Decomposition Methods For Vorticity Transport Equation In Boundary Domain Integral Method

The paper deals with the use of domain decomposition methods in Boundary Domain Integral Method (BDIM) for Navier-Stokes equations of laminar viscous incompressible fluid flow. Since the vorticity transport equation presents the major problem in solving BDIM set of equations, domain decomposition methods are used for its solution. Multiplicative and additive Schwarz iterations are implemented. Partial subdomain problems are computed by the use of Krylov subspace type iterative solvers. Overlapping and non-overlapping subdomain divisions are presented and their effects on convergence of domain decomposition iterative procedures are reported. The new iterative schemes are tested on Poiseuille's flow and Backward facing step flow for various Re number values. 1 Basic theory of Domain Decomposition Method Domain Decomposition Method (DDM) is a relatively old method (Schwarz 1870) and is becoming increasingly popular in modern approximation methods due to high parallelisation capabilities. Similarly as Subdomain technique in BEM it divides the original computational domain into several overlapping or non-overlapping subdomains, which now present partial problems, from which solution over the original domain can be found. The main feature of Domain Decomposition Method is a fact, that solving partial problems is only one step towards the solution of the original system. This follows from a fact, that values of functions and its derivatives on the subdomain interface are not known at the beginning of computation. Through an iterative procedure it is then possible to find the final solution with some combination of calculated values from subdomains. Transactions on Modelling and Simulation vol 9, © 1995 WIT Press, www.witpress.com, ISSN 1743-355X