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