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

Fluids and Materials Seminar

14th January 2021, 2:00 pm – 3:00 pm

Online seminar, Zoom link is sent to the fluids and materials seminar mailing list on Mondays.

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).

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