Solution of advection diffusion equations in two space dimensions by a rational Eulerian Lagrangian localized adjoint method over hexagonal grid
M. Al-Lawatia 11 Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Sultanate of Oman
Received by the editors September 6, 2009 and, in revised form, February 22, 2010.
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.AMS subject classifications: 74S30, 65M60, 65D05
Key words: Advection-diffusion equations, characteristic methods, Eulerian-Lagrangian methods, rational basis functions.