An efficient split-operator scheme for 2-D advection-diffusion simulations using finite elements and characteristics

The 2-D advection-diffusion equation is solved by the split-operator method. In the advection phase, a weighted residual approach is employed to minimize the error generated by interpolations. Computer execution time is reduced by adopting Simpson's rule for some of the numerical integrations in the advection phase and by using an iteration strategy in the diffusion phase, thus avoiding the matrix inversion procedure in each time step. The proposed scheme is validated by test problems where analytic solutions for the 1-D and 2-D advection-diffusion equations are available.