Efficient Solution and Sensitivity Analysis of Partial Differential-Algebraic Equation Systems: Application to Corrosion Pit Initiation

Abstract

A mathematical model based on transport and reaction equations describing initiation of pitting corrosion at a MnS sulfide inclusion in NaCl electrolyte was used as a test problem for development of efficient numerical procedures for corrosion simulation and sensitivity analysis. The equations associated with the corrosion model were formulated by using a reaction invariant approach, which resulted in an index-2 partial differential-algebraic equation (PDAE) system. The original PDAE system was regularized to yield a lower index PDAE system, for which we were able to formulate an effective preconditioner for use in the DASPK 3.0 DAE solver. This approach was found to improve the efficiency of the Krylov iterative solver as well as to provide the parameter sensitivities with little additional effort in comparison with another method reported recently. In agreement with previous findings, the results obtained with this approach indicate that the model is most sensitive to the parameters associated with the heterogeneous dissolution of the sulfide inclusion.