IJPAM: Volume 7, No. 4 (2003)
METHODS FOR THE SOLUTION OF THE TRANSIENT
ADVECTION DIFFUSION EQUATIONS
IN THREE SPACE DIMENSIONS
Department of Mathematics and Statistics
College of Science
Sultan Qaboos University
P.O. Box 36, Al-Khodh 123, SULTANATE OF OMAN
e-mail: allawati@squ.edu.om
Abstract.We present a characteristic method for the solution of the transient
advection diffusion equations in three space-dimensions.
This method uses piecewise tri-linear trial and test functions over
rectangular grids within the framework of the Eulerian Lagrangian
localized adjoint methods (ELLAMs). It therefore maintains the advantages
of previous ELLAM schemes. In particular, 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.
Received: April 14, 2003
AMS Subject Classification: 65M25, 76M25, 35D99
Key Words and Phrases: advection-diffusion equations, characteristic methods, Eulerian Lagrangian methods
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 7
Issue: 4