Comparison of some Lagrangian schemes for the simulation of diffusion in discontinuous media

Jocelyne Erhel (1) , Antoine Lejay (2, 3) , Géraldine Pichot (1)

1 SAGE - Simulations and Algorithms on Grids for Environment
2 IECN - Institut Élie Cartan de Nancy
3 TOSCA - Simuler et calibrer des modèles stochastiques

We study a diffusion process in a 1D discontinuous medium using a random walk approach. Our main contribution is to encompass two existing numerical methods in the unified framework of the Skew Brownian Motion. This theoretical approach allows to detail and justify the derived algorithms. Numerical simulations are performed on two test cases to show that the algorithms can deal with the discontinuity in the diffusion coefficient

Domaines: Analyse numérique [math.NA]

Jocelyne Erhel, Antoine Lejay, Géraldine Pichot. Comparison of some Lagrangian schemes for the simulation of diffusion in discontinuous media. Mamern 2011, May 2011, Saidia, Morocco. pp.319-322. ⟨hal-00642194⟩