An Enhanced Parareal Algorithm for Partitioned Parabolic-Hyperbolic Coupling

Franz Chouly 1 Miguel Angel Fernández 1
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : We present a parallel time‐marching scheme for coupled parabolic‐hyperbolic problems, as a prototype of fluid‐structure interaction problems involving a linear structure and a viscous fluid. No linearity assumption is made on the parabolic side. The classical Parareal scheme is applied to the parabolic part, while the modified algorithm proposed by Farhat et al. [1] is applied to the hyperbolic part. This hybrid Parareal treatment relies on the partitioned formulation of the coupled propagator. Numerical evidence shows that the resulting scheme is stable for a wide range of physical and discretization parameters.
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Conference papers
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https://hal.inria.fr/hal-00793490
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Franz Chouly, Miguel Angel Fernández. An Enhanced Parareal Algorithm for Partitioned Parabolic-Hyperbolic Coupling. International Conference on Numerical Analysis and Applied Mathematics 2009, Sep 2009, Rethymno, Crete, Greece. pp.1517-1520, ⟨10.1063/1.3241387⟩. ⟨hal-00793490⟩

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