The proposed work concerns the numerical approximations of the shallow-water equations with varying topography. The main objective is to introduce an easy and systematic technique to enforce the well-balance property and to make the scheme able to deal with dry areas. To access such an issue, the derived numerical method is obtained by involving the free surface instead of the water height and ...

Abstract A quasi–second-order scheme is developed to obtain approximate solutions of the two-dimensional shallow water equations (SWEs) with bathymetry. The based on a staggered finite volume space discretization: scalar unknowns are located in discretization cells while vector edges mesh. monotonic upwind-central for conservation laws (MUSCL)-like interpolation discrete convection operators he...

We consider the magnetic induction equation for the evolution of a magnetic field in a plasma where the velocity is given. The aim is to design a numerical scheme which also handles the divergence constraint in a suitable manner. We design and analyze an upwind scheme based on the symmetrized version of the equations in the non-conservative form. The scheme is shown to converge to a weak soluti...

Direct numerical simulation of the receptivity of hy-personic boundary-layers to freestream disturbances requires high-order accurate numerical methods to resolve a wide range of time and length scales. Traditional second-order nite diierence schemes do not have an adequate accuracy level for the direct numerical simulation. In addition, hypersonic ow simulation needs to resolve unsteady bow sh...

This paper concerns the numerical schemes describing solute transport in fissured systems which are characterized by the tectonic blocks and spatial repartition of hydraulic properties with dual permeability structures composed of highand low-permeability blocks of the chalk aquifer (Northern France). Both advection and diffusion mechanisms are taken into account. The novel mathematical approac...