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Volume 9, Issue 1
Solution of Advection Diffusion Equations in Two Space Dimensions by a Rational Eulerian Lagrangian Localized Adjoint Method over Hexagonal Grid

M. Al-Lawatia

Int. J. Numer. Anal. Mod., 9 (2012), pp. 43-55.

Published online: 2012-09

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  • Abstract

We present a characteristic method for the solution of the transient advection diffusion equations in two space-dimensions. This method uses Wachspress-type rational basis functions over hexagonal grids within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes and generates accurate numerical solutions even if large time steps are used in the simulation. Numerical experiments are presented to illustrate the performance of this method and to investigate its convergence numerically.

  • Keywords

Advection-diffusion equations, characteristic methods, Eulerian-Lagrangian methods, rational basis functions.

  • AMS Subject Headings

74S30, 65M60, 65D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-43, author = {M. Al-Lawatia}, title = {Solution of Advection Diffusion Equations in Two Space Dimensions by a Rational Eulerian Lagrangian Localized Adjoint Method over Hexagonal Grid}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {1}, pages = {43--55}, abstract = {

We present a characteristic method for the solution of the transient advection diffusion equations in two space-dimensions. This method uses Wachspress-type rational basis functions over hexagonal grids within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes and generates accurate numerical solutions even if large time steps are used in the simulation. Numerical experiments are presented to illustrate the performance of this method and to investigate its convergence numerically.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/610.html} }
TY - JOUR T1 - Solution of Advection Diffusion Equations in Two Space Dimensions by a Rational Eulerian Lagrangian Localized Adjoint Method over Hexagonal Grid AU - M. Al-Lawatia JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 43 EP - 55 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/610.html KW - Advection-diffusion equations, characteristic methods, Eulerian-Lagrangian methods, rational basis functions. AB -

We present a characteristic method for the solution of the transient advection diffusion equations in two space-dimensions. This method uses Wachspress-type rational basis functions over hexagonal grids within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes and generates accurate numerical solutions even if large time steps are used in the simulation. Numerical experiments are presented to illustrate the performance of this method and to investigate its convergence numerically.

M. Al-Lawatia. (2012). Solution of Advection Diffusion Equations in Two Space Dimensions by a Rational Eulerian Lagrangian Localized Adjoint Method over Hexagonal Grid. International Journal of Numerical Analysis and Modeling. 9 (1). 43-55. doi:
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