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Conservative Semi-Lagrangian Advection on Adaptive Unstructured Meshes

Iske, A., and M. Käser (2004), Conservative Semi-Lagrangian Advection on Adaptive Unstructured Meshes, Numerical Methods for Partial Differential Equations, 20, 388-411, doi:10.1002/num.10100.

Abstract
A conservative semi-Lagrangian method is designed in order to solve linear advection equations in two space variables. The advection scheme works with finite volumes on an unstructured mesh, which is given by a Voronoi diagram. Moreover, the mesh is subject to adaptive modifications during the simulation, which serves to effectively combine good approximation quality with small computational costs. The required adaption rules for the refinement and the coarsening of the mesh rely on a customized error indicator. The implementation of boundary conditions is addressed. Numerical results finally confirm the good performance of the proposed conservative and adaptive advection scheme.
BibTeX
@article{id589,
  author = {A. Iske and M. K{\"a}ser},
  journal = {Numerical Methods for Partial Differential Equations},
  pages = {388-411},
  title = {{Conservative Semi-Lagrangian Advection on Adaptive Unstructured Meshes}},
  volume = {20},
  year = {2004},
  doi = {10.1002/num.10100},
}
EndNote
%0 Journal Article
%A Iske, A.
%A Käser, M.
%D 2004
%V 20
%J Numerical Methods for Partial Differential Equations
%P 388-411
%T Conservative Semi-Lagrangian Advection on Adaptive Unstructured Meshes
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Printed 21. Aug 2019 15:31