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International Journal of Computer Mathematics Volume 89, 2012 - Issue 3: TOPICS OF CONTEMPORARY COMPUTATIONAL MATHEMATICS
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Section B

Modelling of the advection–diffusion equation with a meshless method without numerical diffusion

Luis Gavete Departamento de Matemática Aplicada a los Recursos Naturales, Universidad Politécnica de Madrid, Madrid, SpainCorrespondence[email protected]
,
Francisco Ureña Departamento de Matemática Aplicada, Universidad de Castilla-La Mancha, Ciudad Real, Spain
,
Juan José Benito Departamento de Construcción y Fabricación, Universidad Nacional de Educación a Distancia, Madrid, Spain
&
María Lucía Gavete Departamento Bioquímica, Fisiología y Genética Molecular, Universidad Rey Juan Carlos, Madrid, Spain
Pages 377-389 | Received 25 Aug 2010, Accepted 02 May 2011, Published online: 27 Jul 2011
 
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Abstract

A comprehensive study is presented regarding the stability of the forward explicit integration technique with generalized finite-difference spatial discretizations, free of numerical diffusion, applied to the advection–diffusion equation. The modified equivalent partial differential equation approach is used to demonstrate that the approximation is free of numerical diffusion. Two-dimensional results are obtained using the von Neumann method of stability analysis. Numerical results are presented showing the accuracy obtained.

2000 AMS Subject Classifications :

Acknowledgements

The authors acknowledge the support from Ministerio de Ciencia e Innovación of Spain, project CGL2008-01757/CLI.

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