Adaptive split-operator methods for modeling transport phenomena in porous medium systems

Split-operator methods are commonly used to approximate environmental models. These methods facilitate the tailoring of different approximation approaches to different portions of the differential operator and provide a means to split large coupled problems into pieces that are more amenable to parallel computation than the original fully-coupled problem. However, split-operator methods introduce an additional source of approximation error into the solution, which is typically either ignored or controlled heuristically. In this work, we develop two methods to estimate and control the error in split-operator methods, which lead to a dynamic adjustment of the temporal splitting step based upon the error estimators. The proposed methods are shown to yield robust solutions that provide the desired control of error. In addition, for a typical nonlinear reaction problem, the new methods are shown to reduce the solution error by more than two orders of magnitude compared to standard methods for an identical level of computational effort. The algorithms introduced and evaluated have widespread applicability in environmental modeling.

► A general algorithm is developed to estimate and control operator splitting error. ► Several instances of the algorithm are developed and investigated. ► The adaptive split-operator methods developed are shown to be robust and efficient. ► The advancement of an extrapolated higher order solution was found to be very efficient for a reactive transport problem.