SUMMARYThis paper studies the application of two‐level Schwarz algorithms to several models of computational fluid dynamics. The purpose is to build an algorithm suitable for elliptic and convective models. The subdomain approximated solution relies on the incomplete lower‐upper factorization. The algebraic coupling between the coarse grid and the Schwarz preconditioner is discussed. The deflation method and the balancing domain decomposition method are studied for introducing the coarse‐grid correction as a preconditioner. Standard coarse grids are built with the characteristic or indicator functions of the subdomains. The building of a set of smooth basis functions (analogous to smoothed‐aggregation methods) is considered. A first test problem is the Poisson problem with a discontinuous coefficient. The two options are compared for the standpoint of coarse‐grid consistency and for the gain in scalability of the global Schwarz iteration. The advection–diffusion model is then considered as a second test problem. Extensions to compressible flows (together with incompressible flows for comparison) are then proposed. Parallel applications are presented and their performance measured. Copyright © 2012 John Wiley & Sons, Ltd.

SUMMARYWe use here a reconnection ALE (ReALE) strategy to solve hydrodynamic compressible flows in cylindrical geometries. The main difference between the classical ALE and the ReALE method is the rezoning step where we allow change in the topology. This leads for ReALE to a polygonal mesh, which follows more efficiently the flow. We present here a new displacement of generators in order to keep the Lagrangian features, which are usually lost using ALE with fixed topology. The reconnection capability allows to deal with complex geometries and high-vorticity problems contrary to ALE method. The main difficulty of ReALE is the remapping step where we have to remap physical variables on a mesh with a different topology. For this step, a new remapping method based on a swept intersection algorithm has been developed in the case of planar geometries. We present here the extension of the swept intersection-based remapping method to cylindrical geometries. We demonstrate that our method can be applied to several numerical examples up to problem representative of hydrodynamic experiments.

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