Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem
Article first published online: 19 MAR 2014
Copyright © 2014 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids
Volume 75, Issue 6, pages 446–465, 30 June 2014
How to Cite
Tayachi, M., Rousseau, A., Blayo, E., Goutal, N. and Martin, V. (2014), Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem. Int. J. Numer. Meth. Fluids, 75: 446–465. doi: 10.1002/fld.3902
- Issue published online: 9 MAY 2014
- Article first published online: 19 MAR 2014
- Manuscript Accepted: 16 FEB 2014
- Manuscript Revised: 6 FEB 2014
- Manuscript Received: 24 SEP 2013
- dimensionally heterogeneous coupling;
- domain decomposition;
- multiscale analysis
In the present work, we propose and analyse an efficient iterative coupling method for a dimensionally heterogeneous problem. We consider the case of a 2D Laplace equation with non-symmetric boundary conditions coupled with a corresponding 1D Laplace equation. We first show how to obtain the 1D model from the 2D one by integration along one direction, by analogy with the link between shallow water equations and the Navier–Stokes system. Then we focus on the design of a Schwarz-like iterative coupling method. We discuss the choice of boundary conditions at coupling interfaces. We prove the convergence of such algorithms and give some theoretical results related to the choice of the location of the coupling interface, and to the control of the difference between a global 2D reference solution and the 2D coupled solution. These theoretical results are illustrated numerically. Copyright © 2014 John Wiley & Sons, Ltd.