Solution of advection diffusion equations in two-space dimensions by a rational Eulerian-Lagrangian localized adjoint method over pentagonal grids.
Author
Al-Alawi, Sulaiman Said Humaid.
Publisher
Sultan Qaboos University.
English abstract
Eulerian-Lagrangian localized adjoint methods (ELLAM) are a class
of characteristic methods that have been shown to be effective in
solving advection-dominated transport equations. In this thesis, we
present an ELLAM method for the solution of the two-dimensional
transient advection diffusion equation which uses Wachspress type
rational basis functions over non-uniform pentagonal discretizations
of the spatial domain. The derived scheme maintains the advantages
of previous ELLAM methods and generates accurate numerical solutions for the model equations even when 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 using standard test problems with known analytical solutions.
