SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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A parareal multiscale coupling of finite element and Lattice Boltzmann methods

F. Chouly, M. Astorino, A. Lozinski and A. Quarteroni

Abstract
We present a new numerical procedure for the simulation of time-dependent problems based on the coupling between the finite element method and the Lattice Boltzmann method. The two methods are regarded as macroscale and mesoscale solvers, respectively. The procedure is based on the parareal paradigm and allows for a truly multiscale coupling between two numerical methods having optimal efficiency at different space and time scales. The main motivation, among other, is that one technique may be more efficient, or physically more appropriate or less memory consuming than the other depending on the target of the simulation and/or on the sub-region of the computational domain. We detail the theoretical and numerical framework for linear parabolic equations. We show various numerical examples that will validate the proposed procedure and illustrate its advantages. Finally some recent extensions will be discussed.

Organized by         Universidad de Valladolid     IMUVA