Volume 2 N°2 (2005)

Full title: Axisymmetric finite volumes for the numerical simulation of bulk CO2 transport and assimilation in a leaf

Abstract: This paper deals with the numerical simulation of CO2 transport in the leaf. We study a mathematical model of the diffusion and photosynthesis processes, and present the implementation of an axisymmetric cell centred finite volume scheme for their numerical simulation. The resulting code enables the computation of the lateral diffusion coefficient in the leaf porous medium, from experimental measurements which yield the point wise value of internal CO2 concentration. Hence our model and numerical code allow the analysis of the role of the internal diffusion in the photosynthesis process. We show here that under moderate light, CO2 does not diffuse across long distances because it is rapidly assimilated by photosynthesising cells.

Date of publication : September 2005

Paper presented by Professor Fayssal Benkhaldoun

Abstract:

In the present work, we consider the numerical approximations of multi-fluid compressible fluctuating flows. Assuming that the flow is composed by non mixing compressible fluids, we derived a modellization that can be view as an extension of the standard compressible (k, epsilon) one. This model is fundamentally in non conservation form (the coupling between fluids and turbulence involves non conservative products) and the usual finite volume methods fail. The nonlinear projection scheme is used to preserve, at the discrete level, the main properties of the model. The numerical computations are performed on the Richtmeyer-Meshkov instability to validate the approach and to measure the influence of fluctuations.

Date of publication : May 2005

Paper presented by: Professor Jean Marc Herard

Abstract: In this paper we study the convergence of a streamline method for an hyperbolic problem. Our motivation for this method arises from the problem of simulating multi-phase flow in porous media.

In fact, the streamline method has been applied successfully to reservoir simulation. There is however no study of the convergence of this method. We prove the convergence in a simplified case. In particular, we assume that the velocity depends only on the space variable.

Date of publication : February 2005

Paper presented by Professor Jean-Marc Herard