Schwarz Methods for the Unsteady Compressible Navier Stokes Equations on Unstructured Meshes

Overlapping Schwarz is a family of preconditioners for solving large sparse linear systems arising from the discretization of partial di erential equations see e g CS DW SBG Here we report on our preliminary experiences on using it in the implicit solution of unsteady Navier Stokes N S equations discretized on two dimensional unstructured meshes One of the advantages of implicit methods is that they allow the time steps to be determined solely based on the physics of the uid ow not on the stability property of the time discretization scheme Ven VM To advance in time a large linear system of equations must be solved Depending of the size of the time step and other ow parameters the conditioning of the matrix may change drastically from time step to time step To solve these systems iteratively it is necessary to have a family of preconditioners whose strength can be controlled Overlapping Schwarz methods do have these properties for