Numerical simulation of steady-state ion transfer to rotating disk electrode: Accuracy and computational efficiency

The effect of the parameters of difference scheme (the method of approximation of space derivatives, the initial grid step, the coefficient of grid step nonuniformity, the length of computational region) and the method of solving difference equations on the accuracy and computational efficiency of simulating steady-state ion transfer to a rotating disk electrode is analyzed. The dependences of the error of numerical solution on the parameters of difference scheme were obtained for various Schmidt numbers. It is shown that available approximate equations for hydrodynamic velocity yield an error of 1–0.01%, which restricts the accuracy of numerical simulation when the number of grid nodes exceeds 100. The Newman method involving simultaneous solution of difference equations and the method of splitting (the equations of ion transfer are solved one after another and independently of one another at each iteration) are compared. It is shown that the method of splitting is efficient at a small difference between the diffusion coefficients, a large number of types of ions, and relatively low accuracy.