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

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.

Keywords:

• advection–diffusion
• generalized finite difference

2000 AMS Subject Classifications :

• 65M06
• 65M12
• 76M20

Acknowledgements

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