Stéphane Popinet

A vertically-Lagrangian, non-hydrostatic, multilayer model for multiscale free-surface flows

I will present a semi-discrete, multilayer set of equations
describing the three-dimensional motion of an incompressible fluid
bounded below by topography and above by a moving free-surface. This
system is a consistent discretisation of the incompressible Euler
equations, valid without assumptions on the slopes of the interfaces.
Expressed as a set of conservation laws for each layer, the
formulation has a clear physical interpretation and makes a seamless
link between the hydrostatic Saint-Venant equations, dispersive
Boussinesq-style models and the incompressible Euler equations. The
associated numerical scheme, based on an approximate vertical
projection and multigrid-accelerated column relaxations, provides
accurate and efficient solutions for all regimes. The same model can
thus be applied to study metre-scale waves, even beyond breaking, with
results closely matching those obtained using small-scale
Euler/Navier-Stokes models, and coastal or global scale dispersive
waves, with an accuracy and efficiency comparable to extended
Boussinesq wave models. The implementation is adaptive, parallel and
open source as part of the Basilisk framework (basilisk.fr).