PENEL , Yohan

When one solves PDEs modelling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. For instance, the underlying physical assumptions for the Euler equations are the positivity...

In geophysics, the shallow water model is a good approximation of the incompressible Navier-Stokes system with free surface and it is widely used for its mathematical structure and its computational efficiency. However, applications of this model are restricted by two approximations under which it was derived, namely the hydrostatic pressure...

In some configurations, dispersion effects must be taken into account to improve the simulation of complex fluid flows. A family of free-surface dispersive models has been derived in Fernández-Nieto et al. (Commun Math Sci 16(05):1169–1202, 2018). The hierarchy of models is based on a Galerkin approach and parameterised by the number of...

A new family of non-hydrostatic layer-averaged models for the non-stationary Euler equations is presented in this work, with improved dispersion relations. They are a generalisation of the layer-averaged models introduced in Fernández-Nieto et al. (Commun Math Sci 16(05):1169–1202, 2018), named LDNH models, where the vertical profile of the...

A new family of non-hydrostatic layer-averaged models for the non-stationary Euler equations is presented in this work, with improved dispersion relations. They are a generalisation of the layer-averaged models introduced in Fernández-Nieto et al. (Commun Math Sci 16(05):1169–1202, 2018), named LDNH models, where the vertical profile of the...