Semi-Lagrangian method for advection problem with adaptive grid

In the paper, the semi-Lagrangian method is considered for the numerical solution of the advection problem. A numerical solution is constructed as a piecewise constant function on a rectangular grid. The proposed method is stable and gives an approximate solution with the first order of accuracy. To...

Full description

Saved in:
Bibliographic Details
Main Authors: Efremov, A., Karepova, E., Shaydurov, V., Vyatkin, A.
Format: Conference Proceeding
Language:English
Subjects:
Advection
Grid refinement (mathematics)
Smoothing
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In the paper, the semi-Lagrangian method is considered for the numerical solution of the advection problem. A numerical solution is constructed as a piecewise constant function on a rectangular grid. The proposed method is stable and gives an approximate solution with the first order of accuracy. To reduce the effect of smoothing an approximate solution because of numerical viscosity, a mesh refinement is applied in the vicinity of large gradients of the approximate solution. The localization of the smoothing effect is illustrated by a numerical example. In contrast to the traditional Eulerian schemes, semi-Lagrangian algorithms do not involve a time step restriction.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4964997