ANGOT, Philippe; CALTAGIRONE, Jean-Paul; FABRIE, Pierre

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ANGOT, Philippe
Institut de Mathématiques de Marseille [I2M]

CALTAGIRONE, Jean-Paul

FABRIE, Pierre
Institut de Mathématiques de Bordeaux [IMB]

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Turbulence and Interactions, Proceedings of the TI 2015 conference, 4th International Conference on Turbulence and Interactions, 2015-11-02, Cargèse (Corsica).

Springer

Résumé en anglais

We present the main features and sharp numerical applications of the fast vector penalty-projection methods (VPP ε) [1, 2, 3], based on three key ideas explained further. In particular, we proposed new fast Helmholtz-Hodge decompo-sitions of L 2-vector fields in bounded domains by solving vector elliptic problems penalized with suitable adapted right-hand sides [4]. This procedure, used as an approximate divergence-free velocity projection step, yields a velocity divergence vanishing as O(ε δt), δt being the time step. It only requires a few iterations of preconditioned conjugate gradients whatever the spatial mesh step h, if the penalty parameter ε is chosen sufficiently small up to machine precision, e.g. ε = 10 −14. These methods prove to be efficient, fast and robust to accurately compute incom-pressible or low Mach multiphase flows under strong stresses: large mass density, viscosity or anisotropic permeability jumps, strong surface tension inducing large interface deformations, or with open boundary conditions, whereas other methods either cannot reach the suitable mesh convergence and run slower or simply crash.< Réduire

Mots clés en anglais

Vector penalty-projection methods

fast Helmholtz-Hodge decompositions

Navier-Stokes equations

Multiphase flows

incompressible or low-Mach flows

strong stresses

large density or viscosity variations

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A spectacular solver of low-Mach multiphase Navier-Stokes problems under strong stresses

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