Section: New Results

Numerical methods for free-surface flows

A two-dimensional method for a dispersive shallow water model

Participants : Nora Aïssiouene, Marie-Odile Bristeau, Edwige Godlewski, Jacques Sainte-Marie.

We propose a numerical method for a two-dimensional dispersive shallow water system with topography. This model is a depth averaged Euler system and takes into account a non-hydrostatic pressure which implies to solve an incompressible system. From the variational formulation of the mixed problem proposed in [6], we apply a finite element method with compatible spaces to the two-dimensional problem on unstructured grids.

Numerical Discretization for Coriolis Effects

Participants : Emmanuel Audusse, Do Minh Hieu, Yohan Penel.

Efficient computations near the geostrophic equilibrium need to carefully design numerical schemes. This question is investigated in the context of colocated finite volume approach and extends previous works by Bouchut et al.  [32], Dellacherie  [35], Buet and Despres  [36].

Optimization of topography

Participants : Sebastian Reyes-Riffo, Julien Salomon.

We work on a method to compute optimal topographies for wave-energy production. The first part of the work was devoted to the numerical analysis of the scheme used to simulate waves. In this way, we have obtained stability conditions that enable to couple it with an optimization loop.

An adaptive numerical scheme for solving incompressible two-phase and free-surface flows

Participant : Dena Kazerani.

We present a numerical scheme for solving two-phase or free surface flows. The interface/free surface is modelled using the level-set formulation. Besides, the mesh is anisotriopic and adapted at each iteration. The incompressible Navier–Stokes equations are temporally discretized using the method of characteristics and are solved at each time iteration by a first order Lagrange–Galerkin method. The level-set function representing the interface/free surface satisfies an advection equation which is also solved using the method of characteristics.

Propeler design

Participants : Jérémy Ledoux, Julien Salomon.

We work on a usual algorithm in propeler design: based on the so-called “Blade Element Momentum Theory”, this approach reduces the simulation to a 2D system by coupling the latter with a outer loop of low computational cost. So far, this method has not been analyzed mathematically, hence our interest.