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