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Numerical analysis of the advection-diffusion of a solute in random media

Julia Charrier 1
1 SAGE - Simulations and Algorithms on Grids for Environment
Inria Rennes – Bretagne Atlantique , IRISA-D1 - SYSTÈMES LARGE ÉCHELLE
Abstract : We consider the problem of numerically approximating the solution of the coupling of the flow equation in a random porous medium, with the advection-diffusion equation. More precisely, we present and analyse a numerical method to compute the mean value of the spread of a solute introduced at the initial time, and the mean value of the macro-dispersion, defined at the temporal derivative of the spread. We propose a Monte-Carlo method to deal with the uncertainty, i.e. with the randomness of the permeability field. The flow equation is solved using finite element. The advection-diffusion equation is seen as a Fokker-Planck equation, and its solution is approximated thanks to a probabilistic particular method. The spread is indeed the expected value of a function of the solution of the corresponding stochastic differential equation, and is computed using an Euler scheme for the stochastic differential equation and a Monte-Carlo method. Error estimates on the mean spread and on the mean dispersion are established, under various assumptions, in particular on the permeability random field.
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Submitted on : Wednesday, March 30, 2011 - 2:53:21 PM
Last modification on : Tuesday, October 19, 2021 - 11:58:49 PM


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  • HAL Id : inria-00581244, version 1


Julia Charrier. Numerical analysis of the advection-diffusion of a solute in random media. [Research Report] RR-7585, INRIA. 2011, pp.30. ⟨inria-00581244⟩



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