A Novel Physics-Weighted Adaptive Finite Element Method for Numerical Analysis and High-Accuracy Prediction of Localized Corrosion in Protective Nanocomposite Coatings

In this work, numerical methods for the modeling of reactant transport in nanocomposite coated metallic materials are studied and a physics-weighted adaptive finite element framework is proposed to predict localized corrosion behavior. Using a one-dimensional steady-state reaction–diffusion model, we examined the effects of coating thickness and connected porosity on the metal-interface reactant flux. Numerical solutions are obtained by second-order finite-difference discretization for uniform and geometrically graded meshes and are compared with analytical reference solutions. Mesh convergence study showed that the near second-order accuracy was obtained with estimated convergence orders of 2.01 and 1.96 for uniform and graded meshes, respectively. The relative flux error was reduced from 0.7829% to 0.0030% for uniform meshes and from 5.8919% to 0.0261% for graded meshes by increasing the number of elements from 12 to 192. The parametric calculations showed that the transport of reactants decreased significantly with increasing coating thickness and decreasing porosity.