Chimera Type Domain Decomposition Methods Applied to Fractional Step Finite Element Schemes for Incompressible Flows

In this paper, some ideas for solving Navier-Stokes equations using fractional step techniques in combination with domain decomposition methods are introduced. Apart from its traditional use in a rational distribution of the computational work, the domain decomposition (DD) method can be a powerful tool when dealing with complex geometries, which can have moving parts. The CBS (Characteristic Based Split) general algorithm is here used to numerically solve the flow equations in each of the subdomains. It provides the required flexibility for dealing equally well with a broad range of flow regimes: incompressible and compressible, viscous and inviscid, laminar and turbulent, stationary and transient ones. As the same fluid dynamic algorithm is used for solving all these problems, the combined DD + CBS ideas inherite the fluid algorithm flexibility. A special set of transmision conditions for the subdomains and a new conservative interpolation are among the features introduced. In this work, the main ideas are set and some simple laminar incompressible problems are tackled.