Multiscale coupling of finite element and lattice Boltzmann methods for time dependent problems

Matteo Astorino (1) , Franz Chouly (2) , Alfio Quarteroni (3)

1 CMCS - Chair of Modelling and Scientific Computing
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 CMCS-EPFL - CMCS-EPFL

In this work we propose 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 motivations behind this approach are manifold. Among others, we have 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. The theoretical and numerical framework is presented for parabolic equations even though its potential applicability is much wider (e.g. Navier-Stokes equations). Various numerical examples on the heat equation will validate the proposed procedure and illustrate its multiple advantages.

Mots clés: finite element method; lattice Boltzmann method; multiscale coupling; Parareal; parallel-in-time domain decomposition

Domaines: Analyse numérique [math.NA]; Analyse numérique [cs.NA]; Physique Numérique [physics.comp-ph]

Matteo Astorino, Franz Chouly, Alfio Quarteroni. Multiscale coupling of finite element and lattice Boltzmann methods for time dependent problems. 2012. ⟨hal-00746942v1⟩