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A semi-Lagrangian method on dynamically adapted octree meshes
An erratum for this article can be found here:
https://doi.org/10.1515/rnam-2016-0006
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Kirill M. Terekhov
,
Maxim A. Olshanskii
Published/Copyright:
December 8, 2015
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.
Received: 2015-9-28
Accepted: 2015-10-15
Published Online: 2015-12-8
Published in Print: 2015-12-1
© 2015 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Preface
- On the occasion of the 70th anniversary of Yuri A. Kuznetsov
- Original Articles
- High order approximations in space and time of a sixth order Cahn–Hilliard equation
- A fast iteration method for solving elliptic problems with quasiperiodic coefficients
- Numerical simulation of spatial motion of a thread
- Explicit algorithms to solve a class of state constrained parabolic optimal control problems
- A semi-Lagrangian method on dynamically adapted octree meshes
Articles in the same Issue
- Frontmatter
- Preface
- On the occasion of the 70th anniversary of Yuri A. Kuznetsov
- Original Articles
- High order approximations in space and time of a sixth order Cahn–Hilliard equation
- A fast iteration method for solving elliptic problems with quasiperiodic coefficients
- Numerical simulation of spatial motion of a thread
- Explicit algorithms to solve a class of state constrained parabolic optimal control problems
- A semi-Lagrangian method on dynamically adapted octree meshes
