Volume 1 N°1 (2004)

Abstract :

The shallow water model with a source term due to topography gradient is approximated within the frame of Finite Volume numerical methods. The cornerstone of the method is the solution of the inhomogeneous Riemann problem. Thus the numerical scheme can deal simultaneously with discrete steady states, flood, occurrence and covering of dry zones.

We present the parameterization through the discontinuity of topography, emphasizing on the resonance phenomenon. We then build the solution of the inhomogeneous Riemann problem using a continuation method with respect to the jump of topography. Finally, numerical experiments illustrate the agreement of the numerical method with the previous analysis.

Date of publication: April 2004

Paper presented by : Professor Jean-Marc Herard

Abstract :

This paper describes the finite volume method implemented in Code Saturne, Electricite de France general-purpose computational fluid dynamic code for laminar and turbulent flows in complex two and three- dimensional geometries. The code is used for industrial applications and research activities in several fields related to energy production (nuclear power thermal-hydraulics, gas and coal combustion, turbomachinery, heating, ventilation and air conditioning...). The set of equations considered consists of the Navier-Stokes equations for incompressible flows completed with equations for turbulence modelling (eddy-viscosity model and second moment closure) and for additional scalars (temperature, enthalpy, concentration of species, ...).

The time-marching scheme is based on a prediction of velocity followed by a pressure correction step. Equations for turbulence and scalars are resolved separately afterwards. The discretization in space is based on the fully conservative, unstructured fi nite volume framework, with a fully colocated arrangement for all variables. Speci c eff ort has been put into the computation of gradients at cell centres. Industrial applications illustrate important aspects of physical modellingsuch as turbulence (using Reynolds-Averaged Navier-Stokes equations or Large Eddy Simulation), combustion, conjugate heat transfer (coupled with the thermal code SYRTHES ) and fluid-particle coupling with a lagrangian approach. These examples also demonstrate the capability of the code to tackle a large variety of meshes and cell geometries, including hybrid meshes with arbitrary interfaces.

Key words : Navier-Stokes, finite volume, unstructured mesh, colocated arrangement, gradient calculation, turbulent flows, incompressible flows, Reynolds-Averaged Navier-Stokes equations, Large Eddy Simulation, parallel computing, nuclear power, gas and coal combustion, Code Saturne

Date of publication : February 2004

Paper presented by : Professor Jean-Marc Herard

Abstract:

We adapt the Saurel-Abgrall front capturing finite volumes method for an industrial simulation of compressible multifluid flows. We then apply the method to the case of air-water flow in the cooling chamber of an axisymmetrical gas generator. We describe successively how to deal with exact and global Riemann solvers, pressure oscillations, unstructured meshes, axisymmetry, boundary conditions and overly restrictive CFL conditions. The resulting algorithm is efficient and robust.

Date of publication : December 2003

Paper presented by : Professor Thierry Gallouet

Abstract :

It is well known that the solution of the Laplace equation in a non convex polygonal domain of R 2 has a singular behaviour near non convex corners. Consequently we investigate three refined Finite volume methods (cell-center, conforming Finite volume-element and non conforming Finite volume-element) to approximate the solution of such a problem and restore optimal orders of convergence as for smooth solutions. Numerical tests are presented and confirm the theoretical rates of convergence.

Date of publication: October 2003

paper presented by : Professor Raphaele Herbin