High-Order Unconditionally Energy-Stable Decoupled Method for Phase Field Modeling of Pitting Corrosion with Adaptive Implementation

Abstract

Pitting corrosion, recognized as one of the most catastrophic forms of localized corrosion, frequently leads to premature structural failures. A major computational challenge is the development of accurate and efficient numerical methods that can capture both the initiation and the nonlinear evolution of corrosion pits. In this work, we propose a third-order, decoupled, unconditionally energy-stable implicit-explicit (IMEX) Runge-Kutta scheme for a phase-field model of pitting corrosion, which is formulated as a gradient flow of a coupled free energy functional involving a phase field variable and a normalized ion concentration. The proposed scheme is rigorously proven to satisfy a discrete energy dissipation law, regardless of time step size. To further enhance computational performance, we integrate an adaptive mesh refinement and dynamic time-stepping strategy, enabling efficient resolution of interface dynamics. Comprehensive numerical experiments validate the high accuracy, unconditional energy stability, and effectiveness of adaptive implementation in simulating the complex spatio-temporal evolution of pitting corrosion.