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We study several iterative methods for fully coupled flow and reactivetransport in porous media. The resulting mathematical model is a coupled,nonlinear evolution system. The flow model component builds on the Richardsequation, modified to incorporate nonstandard effects like dynamic capillarityand hysteresis, and a reactive transport equation for the solute. The two modelcomponents are strongly coupled. On one hand, the flow affects theconcentration of the solute; on the other hand, the surface tension is afunction of the solute, which impacts the capillary pressure and, consequently,the flow. After applying an Euler implicit scheme, we consider a set ofiterative linearization schemes to solve the resulting nonlinear equations,including both monolithic and two splitting strategies. The latter include acanonical nonlinear splitting and an alternate linearized splitting, whichappears to be overall faster in terms of numbers of iterations, based on ournumerical studies. The (time discrete) system being nonlinear, we investigatedifferent linearization methods. We consider the linearly convergent L-scheme,which converges unconditionally, and the Newton method, convergingquadratically but subject to restrictions on the initial guess. Wheneverhysteresis effects are included, the Newton method fails to converge. TheL-scheme converges; nevertheless, it may require many iterations. This aspectis improved by using the Anderson acceleration. A thorough comparison of thedifferent solving strategies is presented in five numerical examples,implemented in MRST, a toolbox based on MATLAB.

Efficient Solvers for Nonstandard Models for Flow and Transport in Unsaturated Porous Media