Conservative semi-Lagrangian advection on adaptive unstructured meshes

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 simul...

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Bibliographic Details
Published inNumerical methods for partial differential equations Vol. 20; no. 3; pp. 388 - 411
Main Authors Iske, Armin, Käser, Martin
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.05.2004
Subjects
advection equation
conservative scheme
mesh adaptivity
semi-Lagrangian
Voronoi diagram
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Summary: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. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 388–411, 2004
Bibliography:ark:/67375/WNG-6VFDHZWJ-M
istex:DEA0D4CE21ACDFE932066A690D56EB5F6DAAA400
ArticleID:NUM10100
European Union within the project NetAGES (Network for Automated Geometry Extraction from Seismic) - No. IST-1999-29034
ISSN:0749-159X
1098-2426
DOI:10.1002/num.10100