IJPAM: Volume 7, No. 4 (2003)

AN EULERIAN LAGRANGIAN LOCALIZED ADJOINT
METHODS FOR THE SOLUTION OF THE TRANSIENT
ADVECTION DIFFUSION EQUATIONS
IN THREE SPACE DIMENSIONS

Mohamed Al-Lawatia
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