Comparison of fully coupled approaches for approximating nonlinear transport and reaction problems

The purpose of this work is to evaluate the computational efficiency of fully coupled approaches for approximating a common class of nonlinear, two-phase advective–dispersive–reactive equations. The general problem considered includes homogeneous phase chemical kinetics, equilibrium interphase mass transfer, and rate-controlled interphase mass transfer––all of which may be nonlinear. Aspects of the problem investigated include discrete mass conservative formulations, temporal discretization approaches, and nonlinear equation solution methods. Their effect on computational efficiency is investigated through a series of numerical experiments using a nondimensional model problem. The effect of problem characteristics such as large sorption capacity, strong sorption nonlinearity, fast mass transfer, fast reactions, and strong diffusion is investigated. Comparisons of solution efficiency show that the optimal approach depends upon: (1) the characteristics of the problem considered, which may be described in a nondimensional form; and (2) the accuracy achieved in the solution. Results offer general guidance for selecting solution approaches for the class of problems investigated and introduce some new solution approaches to the water resources field that may be applicable to other problems.