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Volume 30, Issue 3
A Higher-Order Eulerian-Lagrangian Localized Adjoint Method for Two-Dimensional Unsteady Advection-Diffusion Problems

Mohamed Al-Lawatia

DOI: 10.4208/jcm.1110-m3465

J. Comp. Math., 30 (2012), pp. 324-336.

Published online: 2012-06

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  • Abstract

We present a higher-order in-space characteristic method for the solution of the transient advection diffusion equations in two space dimensions. This method uses biquadratic trial and test functions within the framework of the Eulerian-Lagrangian localized Adjoint Methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes. Namely, it treats general boundary conditions naturally in a systematic manner, conserves mass, and symmetrizes the governing transport equations. Moreover, it 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 establish its order of convergence numerically.

  • Keywords

Advection-diffusion equations, Characteristic methods, Eulerian-Lagrangian methods, Biquadratic interpolation.

  • AMS Subject Headings

65D30.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-30-324, author = {Mohamed Al-Lawatia}, title = {A Higher-Order Eulerian-Lagrangian Localized Adjoint Method for Two-Dimensional Unsteady Advection-Diffusion Problems}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {3}, pages = {324--336}, abstract = {

We present a higher-order in-space characteristic method for the solution of the transient advection diffusion equations in two space dimensions. This method uses biquadratic trial and test functions within the framework of the Eulerian-Lagrangian localized Adjoint Methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes. Namely, it treats general boundary conditions naturally in a systematic manner, conserves mass, and symmetrizes the governing transport equations. Moreover, it 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 establish its order of convergence numerically.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1110-m3465}, url = {http://global-sci.org/intro/article_detail/jcm/8433.html} }
TY - JOUR T1 - A Higher-Order Eulerian-Lagrangian Localized Adjoint Method for Two-Dimensional Unsteady Advection-Diffusion Problems AU - Mohamed Al-Lawatia JO - Journal of Computational Mathematics VL - 3 SP - 324 EP - 336 PY - 2012 DA - 2012/06 SN - 30 DO - http://doi.org/10.4208/jcm.1110-m3465 UR - https://global-sci.org/intro/article_detail/jcm/8433.html KW - Advection-diffusion equations, Characteristic methods, Eulerian-Lagrangian methods, Biquadratic interpolation. AB -

We present a higher-order in-space characteristic method for the solution of the transient advection diffusion equations in two space dimensions. This method uses biquadratic trial and test functions within the framework of the Eulerian-Lagrangian localized Adjoint Methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes. Namely, it treats general boundary conditions naturally in a systematic manner, conserves mass, and symmetrizes the governing transport equations. Moreover, it 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 establish its order of convergence numerically.

Mohamed Al-Lawatia. (2012). A Higher-Order Eulerian-Lagrangian Localized Adjoint Method for Two-Dimensional Unsteady Advection-Diffusion Problems. Journal of Computational Mathematics. 30 (3). 324-336. doi:10.4208/jcm.1110-m3465
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