Finite-difference Simulation Method Research Articles

Finite-Difference Simulation Method for Waves and Viscous Flows about a Ship

A finite-difference method named WISDAM-II is developed for viscous flow about a steadily advancing ship involving free-surface waves. The Navier-Stokes equations in a rotational form are solved by a time-marching scheme in a boundary-fitted coordinate system which is deformed so as to fit the moving free-surface. Making use of the subgrid-scale turbulence model, the three-dimensional separation and the effect of the free-surface waves on the viscous flow are simulated and discussed.

A comparison of some recently developed procedures for digital simulation in electroanalytical research

Some recently developed digital simulation procedures are compared. The comparison tests are simulations of cyclic voltammetric experiments concerning uncomplicated and complicated electrochemical processes. It is shown that the problems relating to the use of the explicit finite difference simulation method with a conventional uniform space grid are practically cancelled by using exponentially expanding grids, so that minicomputers can be profitably employed. Limitations to the use of the orthogonal collocation technique for simulating coupled chemical reactions are outlined.

Application of the explicit finite difference simulation method to cyclic voltammetry and its use in electroanalytical investigations

The principles of the application of the explicit finite difference simulation method to cyclic voltammetry are described, and the limitations and capabilities of the method are discussed for several examples. The main reactions treated are an e.c. mechanism with the chemical reaction reversible in character, and an e.e. mechanism in which the second reversible charge-transfer competes with a dismutation equilibrium triggered by a subsequent irreversible chemical reaction. Attention is given to the proper notation for use in simulating homogeneous chemical reactions.

An implicit finite difference method simulation of spectro-electrochemical working curves

The problem of digitally simulating concentration profiles of electrogenerated species is examined by an implicit finite difference method. The treatment is developed in a general manner so that a variety of electrochemical problems can be solved with a minimum alteration in existing explicit approaches. The advantage of this method arises from the unrestricted stability criterion on the diffusion coefficient resulting in a dramatic decrease in the required number of calculations necessary to generate a working curve. Improvements of one to two orders of magnitude in efficiency are noted for several examples. The analysis for the internal reflection spectro-electrochemical case is emphasized.

An implicit finite difference method simulation of spectro-electrochemical working curves

Summary The problem of digitally simulating concentration profiles of electrogenerated species is examined by an implicit finite difference method. The treatment is developed in a general manner so that a variety of electrochemical problems can be solved with a minimum alteration in existing explicit approaches. The advantage of this method arises from the unrestricted stability criterion on the diffusion coefficient resulting in a dramatic decrease in the required number of calculations necessary to generate a working curve. Improvements of one to two orders of magnitude in efficiency are noted for several examples. The analysis for the internal reflection spectro-electrochemical case is emphasized.