Iterative Split-Operator Approaches for Approximating Advection Dominated Nonlinear Reactive Transport Problems

Split-operator (SO) approaches are often used to compute numerical solutions to nonlinear reactive solute transport problems. SO methods are timestep-splitting methods that separate the reactive transport problem into transport and reaction sub-problems, thus avoiding many costly matrix operations and allowing the best numerical method to be used for each process. But this uncoupling also introduces an additional source of numerical error, known as the splitting error. In standard (non-iterative) SO approaches, the splitting error is be reduced at the expence of reducing the timestep. By contrast, the iterative split-operator (ISO) algorithm removes the splitting error through iteration. But standard ISO methods can converge quite slowly. In recent work, we have proposed several techniques to accelerate ISO convergence for nonlinear reactive transport problems. These convergence acceleration techniques include solution projection methods and interpolation of lagged operator estimates over a timestep. Theoretical analysis and numerical experiments indicate that a second-order convergence rate can be achieved for problems which are sufficiently smooth. In this presentation we report on efforts to extend the above mentioned techniques to advection dominated transport problems, which are characterized by sharp concentration fronts. We will discuss our efforts to combine the convergence acceleration techniques with several high-resolution finite difference schemes for advective transport.