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
复制标题
半拉格朗日格式中扩散项的高阶处理技术
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
R. Ferretti
中科院分区：
文献类型：
--
作者：
R. Ferretti
在本文中，我们考虑了一种处理可能退化的对流扩散方程的高阶半拉格朗日方法，该方法已由不同的作者以类似的形式提出。该格式基于解的随机表示公式，避免了演化算子中平流和扩散部分的分裂。本文进行了一般的理论分析，特别强调了使用大的Courant数的可能性，并给出了一维和二维的数值试验。AMS科目分类：65M25、65M12、60H30
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