A general method for electrochemical simulations .1. Formulation of the strategy for two-dimensional simulations

A strategy for a general electrochemical simulator is presented based on formulating the finite difference form of coupled mass transport and kinetic equations as a single sparse matrix. A treatment of a general mechanism consisting of first-and second-order homogeneous steps and quasi-reversible heterogeneous couples is developed for both steady-state and transient conditions, This is illustrated for two-dimensional simulations with potential applications including microdisk and channel microband electrodes, though the method may easily be applied to higher or lower dimensions and could include terms describing mass transport due to migration. Nonlinearities due to second-order kinetics are treated using Newton's method with an analytically derived Jacobian. ILU and MILU preconditioned Krylov subspace methods (CGS, BICGSTAB(/), and RGMRES) are used to solve the resulting nonsymmetric sparse linear system. The efficiency of these solvers is compared to ''brute force'' LU factorization, SIP, and multigrid methods for a typical steady-state channel microband problem.