LISSONI , Giulia

We propose a Discrete Duality Finite Volume scheme (DDFV for short) for an energy transport model for semiconductors. As in the continuous case, thanks to a change of variables into the so-called "entropic variables", we are able to prove a discrete entropy-dissipation estimate, which gives a priori estimates for the problem. We perform some...

The goal of this thesis is to study and develop numerical schemes of finite volume type for problems arising in fluid mechanics, namely Stokes and Navier-Stokes problems. The schemes we choosed are of discrete duality type, denoted by DDFV; this method works on staggered grids, where the velocity unknowns are located at the centers of control...

International audience

We consider DDFV discretization of the Navier-Stokes equations where the convection fluxes are computed by means of B-schemes, generalizing the classical centered and upwind discretizations. This study is motivated by the analysis of domain decomposition approaches. We investigate on numerical grounds the convergence of the method.

We propose and analyze non-overlapping Schwarz algorithms for the domain decomposition of the unsteady incompressible Navier-Stokes problem with Discrete Duality Finite Volume discretizations. The design of suitable transmission conditions for the velocity and the pressure is a crucial issue. We establish the well-posedness of the method and...

We propose a Discrete Duality Finite Volume scheme (DDFV for short) for the unsteady incom-pressible Navier-Stokes problem with outflow boundary conditions. As in the continuous case, those conditions are derived from a weak formulation of the equations and they provide an energy estimate of the solution. We prove wellposedness of the scheme...

The aim of this work is to analyze " Discrete Duality Finite Volume " schemes (DDFV for short) on general meshes by adapting the theory known for the linear Stokes problem with Dirichlet boundary conditions to the case of Neu-mann boundary conditions on a fraction of the boundary. We prove well-posedness for stabilized schemes and we derive...

We propose and analyze non-overlapping Schwarz algorithms for the domain decomposition of the unsteady incompressible Navier–Stokes problem with Discrete Duality Finite Volume (DDFV) discretization. The design of suitable transmission conditions for the velocity and the pressure is a crucial issue. We establish the well-posedness of the method...

This study presents a novel approach of surface-to-surface (S2S) radiation in the context of an immersed volume method. Radiating facets are reconstructed from the solid-liquid interface. Obstructed view factors are accurately computed while energy balance is ensured through flux correction. The resulting radiative flux is then coupled with a...

In this paper, we describe an interface reconstruction method in two dimension. This method is an extension of DPIR , which reconstructs continuous interfaces and preserves partial volumes using dynamic programming. First we extend the method to curved interfaces. Then, we present tools to improve its robustness in order to apply it to...