A Technique for High-Order Treatment of Diffusion Terms in Semi-Lagrangian Schemes

A Technique for High-Order Treatment of Diffusion Terms in Semi-Lagrangian Schemes

Year:    2010

Communications in Computational Physics, Vol. 8 (2010), Iss. 2 : pp. 445–470

Abstract

We consider in this paper a high-order, semi-Lagrangian technique to treat possibly degenerate advection-diffusion equations, which has been proposed in similar forms by various authors. The scheme is based on a stochastic representation formula for the solution, which allows to avoid the splitting between advective and diffusive part of the evolution operator. A general theoretical analysis is carried out in the paper, with a special emphasis on the possibility of using large Courant numbers, and numerical tests in one and two space dimensions are presented.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.070709.011209a

Communications in Computational Physics, Vol. 8 (2010), Iss. 2 : pp. 445–470

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords: