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- Title
A semi-Lagrangian method on dynamically adapted octree meshes.
- Authors
Terekhov, Kirill M.; Nikitin, Kirill D.; Olshanskii, Maxim A.; Vassilevski, Yuri V.
- Abstract
The paper develops a semi-Lagrangian method for the numerical integration of the transport equation discretized on adaptive Cartesian cubic meshes. We use dynamically adaptive graded Cartesian grids. They allow for a fast grid reconstruction in the course of numerical integration. The suggested semi-Lagrangian method uses a higher order interpolation with a limiting strategy and a back-and-forth correction of the numerical solution. The interpolation operators have compact nodal stencils. In a series of experiments with dynamically adapted meshes, we demonstrate that the method has at least the second-order convergence and acceptable conservation and monotonicity properties.
- Subjects
LAGRANGIAN functions; NUMERICAL integration; INTERPOLATION; OCTREES (Computer graphics); NUMERICAL analysis
- Publication
Russian Journal of Numerical Analysis & Mathematical Modelling, 2015, Vol 30, Issue 6, p363
- ISSN
0927-6467
- Publication type
Article
- DOI
10.1515/rnam-2015-0033