A Spectacular Vector Penalty-Projection Method for Darcy and Navier-Stokes Problems
Language
en
Communication dans un congrès
This item was published in
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)
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Vector penalty-projection
Penalty method
Splitting method
Multiphase Navier-Stokes/Brinkman
Anisotropic Darcy problem
Incompressible flows
Origin
Hal imported