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

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

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

FABRIE, Pierre
Institut de Mathématiques de Bordeaux [IMB]

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Finite Volumes for Complex Applications VI - Problems & Perspectives, Finite Volumes for Complex Applications VI - Problems & Perspectives, International Symposium FVCA6, 2011-06-06, Prague. 2011-06, vol. 4, n° 1, p. 39-47

Springer-Verlag (Berlin)

Résumé en anglais

We present a new fast vector penalty-projection method (VPP$_{\eps}$), issued from noticeable improvements of previous works [7, 3, 4], to efficiently compute the solution of unsteady Navier-Stokes/Brinkman problems governing incompressible multiphase viscous flows. The method is also efficient to solve anisotropic Darcy problems. 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 two-step approximate divergence-free vector projection yielding a velocity divergence vanishing as $\mathcal{O}(\eps\, \dt)$, $\dt$ being the time step, with a penalty parameter $\eps$ as small as desired until the machine precision, e.g. $\eps= 10^{−14}$, whereas the solution algorithm can be extremely fast and cheap. The method is numerically validated on a benchmark problem for two-phase bubble dynamics 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 robust method running faster than usual methods and being able to efficiently compute accurate solutions to sharp test cases whatever the density, viscosity or anisotropic permeability jumps, whereas other methods crash.< Réduire

Mots clés en anglais

Vector penalty-projection

Penalty method

Splitting method

Multiphase Navier-Stokes/Brinkman

Anisotropic Darcy problem

Incompressible flows

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A Spectacular Vector Penalty-Projection Method for Darcy and Navier-Stokes Problems

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