Dolomites Research Notes on Approximation

Phase field models have been widely considered to simulate corrosion dynamics characterised by moving boundaries. The benefits of using these models rely on the fact that the moving interface is implicitly treated by means of the introduction of an auxiliary variable. However, the computational cost of these methods is typically very high. In this paper we consider a model for pitting corrosion of a metallic specimen immersed in an electrolytic solution. For its numerical solution we consider a method that relies on a suitable splitting of the governing equations and on the use of exponential integrators. The use of modern MATLAB functions to evaluate the effect of matrix exponentials on a vector is crucial for the efficient implementation of the method. The software used is presented and discussed in detail, and some numerical tests are introduced to show the performance of the proposed algorithms.