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A numerical scheme for diffusion processes in porous media

Lionel Lenôtre 1
1 SAGE - Simulations and Algorithms on Grids for Environment
Inria Rennes – Bretagne Atlantique , IRISA-D1 - SYSTÈMES LARGE ÉCHELLE
Abstract : By nature, porous media are extremely heterogeneous.The lack of precise description and the presence of large scale physical phenoma imply the use of numerical simulation [Beaudoin et al., 2010]. In this talk, we will consider a one-dimensional advection-diffusion equation who involves piecewise constant coefficients. The main difficulty comes from the discontinuity who reflects the problem of multiple layers in the ground. Without drift term, the Skew Brownian Motion permits to develop several exact algorithms with constant time step [Lejay and Pichot, 2012]. Our work will mainly rely on the methods for adding the drift term and the possibility to treat higher dimensional problems. We will discuss existing methods [Etoré and Martinez, 2013] and propose few benchmark tests.
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https://hal.inria.fr/hal-00907563
Contributor : Géraldine Pichot <>
Submitted on : Thursday, November 21, 2013 - 2:18:49 PM
Last modification on : Tuesday, June 15, 2021 - 4:26:19 PM

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  • HAL Id : hal-00907563, version 1

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Lionel Lenôtre. A numerical scheme for diffusion processes in porous media. IMACS 2013, 2013, Annecy-le-Vieux, France. ⟨hal-00907563⟩

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