Volume 8, Issue 2
A Technique for High-Order Treatment of Diffusion Terms in Semi-Lagrangian Schemes

Roberto Ferretti

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

Published online: 2010-08

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  • 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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@Article{CiCP-8-445, author = {}, title = {A Technique for High-Order Treatment of Diffusion Terms in Semi-Lagrangian Schemes}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.070709.011209a}, url = {http://global-sci.org/intro/article_detail/cicp/7580.html} }
TY - JOUR T1 - A Technique for High-Order Treatment of Diffusion Terms in Semi-Lagrangian Schemes JO - Communications in Computational Physics VL - 2 SP - 445 EP - 470 PY - 2010 DA - 2010/08 SN - 8 DO - http://doi.org/10.4208/cicp.070709.011209a UR - https://global-sci.org/intro/article_detail/cicp/7580.html KW - AB -

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.

Roberto Ferretti. (2020). A Technique for High-Order Treatment of Diffusion Terms in Semi-Lagrangian Schemes. Communications in Computational Physics. 8 (2). 445-470. doi:10.4208/cicp.070709.011209a
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