Gas phase appearance and disappearance as a problem with complementarity constraints

TL;DR

This paper applies the Newton-min method to model hydrogen migration in nuclear waste storage, demonstrating its quadratic convergence and efficiency in solving nonlinear PDEs with complementarity constraints.

Contribution

It introduces the application of the Newton-min method to a complex geoscience problem involving nonlinear PDEs with complementarity constraints.

Findings

Newton-min method is quadratically convergent for this problem.

The method is efficient and applicable to hydrogen migration modeling.

Numerical experiments validate the approach's effectiveness.

Abstract

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. This article shows how to apply a modern and efficient solution strategy, the Newton-min method, to this geoscience problem and investigates its applicability and efficiency. In particular, numerical experiments show that the Newton-min method is quadratically convergent for this problem.