A mixed, scalable domain decomposition method for incompressible flow

Abstract

This work deals with the construction of a mixed and extensible domain decomposition method for incompressible flows. In the scheme proposed here, the solution is sought at the intersection of two spaces, one containing the solution of the Navier-Stokes equations considered separately in each subdomain, and the other one containing the solutions of the compatibility equations on the interfaces. A solution verifying all the equations of the two spaces is achieved iteratively. One difficulty is that the interface problem is large and dense. In order to reduce its cost while maintaining the extensibility of the method, we defined an interface macroproblem in terms of a few interface macro unknowns. The best option takes advantage of the incompressibility condition to prescribe an interface macroproblem which propagates the information to the whole domain by making use of only two unknowns per interface. Several examples are used to illustrate the main properties of the method.