Higher-order spatial discretisations in electrochemical digital simulations. Part 4. Discretisation on an arbitrarily spaced grid
A systematic approach to the construction of finite difference formulae for the approximation to first and second derivatives with respect to space on an arbitrarily spaced grid is presented. The finite difference formulae, combined with backward implicit (BI) and extrapolation methods, are used for electrochemical simulations and tested for efficiency. Excellent results are obtained with second and third order discretisations even for very small space intervals in the vicinity of the electrode and strongly expanding grid spacings. This ensures efficient simulation of kineticdiffusion systems where, due to a fast homogeneous reaction, a thin reaction layer is formed adjacent to the electrode.
extrapolation finite difference electrochemical digital simulation high-order spatial discretisation unequal grid