A vertically-Lagrangian, non-hydrostatic, multilayer model for multiscale free-surface flows
Abstract: 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).