In EEG/MEG source analysis, a mathematical dipole is widely used as the “atomic” structure of the primary current distribution. When using realistic finite element models for the forward problem, the current dipole introduces a singularity on the right-hand side of the governing differential equation that has to be treated specifically. We evaluated and compared three different numerical approa...

We study a simple one-dimensional (1-D) toy model for landslides-generated nonlinear water waves. The landslide is modeled as a rigid bump translating down the side of the bottom while the water motion is modeled by the Saint-Venant system of shallow water equations. The resulting system is numerically solved using a well-balanced positivity preserving central-upwind scheme. The obtained numeri...

This paper deals with the regulation problem of a class of irrigation canals using the Saint-Venant partial differential equations (pde). The Internal Model Boundary Control (IMBC) approach is used and the multireaches case is considered (several reaches in cascade). Perturbation theory of exponential semigroup used for control synthesis is extended here to nonhomogeneous hyperbolic systems, as...

In this paper we construct a numerical solver for the Saint Venant equations. Special attention is given to the balancing of the source terms, including the bottom slope and variable crosssectional profiles. Therefore a special discretization of the pressure law is used, in order to transfer analytical properties to the numerical method. Based on this approximation a wellbalanced solver is deve...

We present a new hybrid numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. The idea behind the new finite-volume-particle (FVP) method is to use different schemes for the flow and the pollution computations: the shallow water e...

The study of mechanisms that allow the formation of structures such as sand dunes and ripples at the bottom of a fluid flow plays a crucial role in the understanding of coastal dynamics. The modeling of these phenomena is particularly complex since we must not only solve the Navier-Stokes or Saint-Venant equations with equation for sediment transport, but also take into account the evolution of...

Due to computational issues associated with the free surface NavierStokes or Euler equations, the simulations of geophysical flows are often carried out with shallow water type models of reduced complexity. Thus the hydrostatic assumption for shallow water flows leads to non-linear hyperbolic systems of Saint-Venant type [1]. For these vertically averaged models, efficient and robust numerical ...

English version: Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. Among them, the hydrostatic reconstruction proposed in [1], coupled with a positive numerical flux, allows to verify important mathematical and physical properties like the positivity of the water height and, thus, to avoid unstabilities when dealing wi...