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

doi:10.1016/j.aml.2012.01.037

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ANGOT, Philippe
Laboratoire d'Analyse, Topologie, Probabilités [LATP]

CALTAGIRONE, Jean-Paul
Transferts, écoulements, fluides, énergétique [TREFLE]

FABRIE, Pierre
Équipe EDP et Physique Mathématique

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Applied Mathematics Letters. 2012-11, vol. 25, n° 11, p. 1681--1688

Elsevier

Résumé en anglais

We present a new {\em fast vector penalty-projection method (VPP$_{\eps}$)} to efficiently compute the solution of unsteady Navier-Stokes problems governing incompressible multiphase viscous flows with variable density and/or viscosity. The key idea of the method is to compute at each time step an accurate and curl-free approximation of the pressure gradient increment in time. This method performs a {\em two-step approximate divergence-free vector projection} yielding a velocity divergence vanishing as $\cO(\eps\,\dt)$, $\dt$ being the time step, with a penalty parameter $\eps$ as small as desired until the machine precision, {\em e.g.} $\eps=10^{-14}$, whereas the solution algorithm can be extremely fast and cheap. Indeed, the proposed {\em vector correction step} typically requires only a few iterations of a suitable preconditioned Krylov solver whatever the spatial mesh step. The method is numerically validated on three benchmark problems for non-homogeneous or multiphase flows where we compare it to the Uzawa augmented Lagrangian (UAL) and scalar incremental projection (SIP) methods. Moreover, a new test case for fluid-structure interaction problems is also investigated. That results in a very robust method running faster than usual methods and being able to efficiently and accurately compute sharp test cases whatever the density, viscosity or anisotropic permeability jumps, whereas other methods crash.< Réduire

Mots clés en anglais

Vector penalty-projection method

Divergence-free penalty-projection

Penalty method

Splitting prediction-correction scheme

Navier-Stokes equations

incompressible non-homogeneous or multiphase flows

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A fast vector penalty-projection method for incompressible non-homogeneous or multiphase Navier-Stokes problems

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