On the application of SUPG/θ-method in 2D advection-diffusion-reaction simulation

The SUPG/theta-method for applications in 2D advection-diffusion transport simulation is reviewed and it is presented in details. Spatial discretization is done with finite elements method with stabilized streamline upwind Petrov-Galerkin method, and time discretization was done with theta-stable finite difference operator. Numerical tests showed that this algorithm is general and robust and it can be applied to simulate simple problems of mass transport; for example, pure advection phenomenon in structured mesh, as well as reactive advection-diffusion transport with an unstructured mesh, and not well-behaved velocity field. The method was applied in a simulation of the transport of total phosphorus in the Lake Agua Preta, and the results were validated by comparison with experimental data. The computational cost is directly associated with the value of the safety factor, introduced to assure the stability of the method.