Commun. Comput. Phys., 8 (2010), pp. 445-470.


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

Roberto Ferretti 1*

1 Dipartimento di Matematica, Universita di Roma Tre, L.go S. Leonardo Murialdo, 1, 00146 Roma, Italy.

Received 7 July 2009; Accepted (in revised version) 1 December 2009
Available online 7 April 2010
doi:10.4208/cicp.070709.011209a

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.

AMS subject classifications: 65M25, 65M12, 60H30

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Key words: Advection-diffusion equations, stochastic representation, method of characteristics, semi-Lagrangian schemes, high-order schemes, convergence.

*Corresponding author.
Email: ferretti@mat.uniroma3.it (R. Ferretti)
 

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