Nonlinear complementarity constraints for hydrogen-water flow with hydrogen dissolution in porous media

The modeling of migration of hydrogen produced by the corrosion of the nuclear waste packages in an underground storage including the dissolution
of hydrogen involves a set of nonlinear partial differential equations with nonlinear complementarity constraints. A modern
and efficient solution strategy, the Newton-min method, is applied to this geoscientific
problem. We investigate its applicability and efficiency from both theoretical and numerical point of view for solving linear and nonlinear complementarity problems. Numerical and theorical results will be presented to show the ability of our solver.