Figure 3.19 Finite difference molecule for the alternating-directions implicit method (ADI) of solving the two-dimensional diffusion equation. |

The alternating direction implicit method (i.e., ADI) is employed to calculate transverse diffusion in the x direction via second-order-correct finite differences for a second derivative using unknown molar densities at Zk+i-Hence, [Pg.625]

The numerical simulation for this study is based on the alternating direction implicit finite difference method, using an expanding [Pg.199]

G. Sun and C. W. Trueman, Some fundamental characteristics of the one-dimensional alternating-direction-implicit finite-difference-time-domain method, IEEE Trans. Microw. Theory Tech., vol. 52, pp. 46-52, Jan. 2004.doi 10.1109/TMTT.2003.821230 [Pg.165]

Another approach involves using implicit methods (28, 30, 31) for obtaining/(y, k + 1) [e.g., the Crank-Nicolson (32), the //y implicit finite difference (FIFD) (33), and the alternating-direction implicit (ADI) (34) methods] rather than the explicit solution in (B.1.9). In implicit methods, the equations for calculation of new concentrations depend upon knowledge of the new (rather than the old) concentrations. There are a number of examples of the use of such implicit methods in electrochemical problems, such as in cyclic voltammetry (35) and SECM (36). [Pg.805]

This problem was solved semianalytically in terms of two-dimensional (2D) integral equations [2,3] and numerically by using Krylov integrator [4] and the alternating direction implicit (ADI) finite difference method [3,5]. Potentiostatic transients were computed for two limiting cases a diffusion-controlled process and totally irreversible kinetics [3-5]. The analysis of the simulation [Pg.78]

Studies on solidification modeling have been largely directed towards macroscopic phenomena. A variety of numerical techniques have been used for such modeling studies. Among these are the finite difference method (FDM) with or without the alternate direction implicit (ADI) time-stepping scheme, the FEM, the boundary element method (BEM), the direct finite difference method (DFDM), and the control volume element (VFM) method. [Pg.338]

Menon and Landau [52] developed a model to describe transient diffusion and migration in stagnant binary electrolytes. Nonuniformity at a partially masked cathode was found to increase during electrolysis as the diffusion resistance develops. The calculations were done using an alternating-direction implicit (ADI) finite difference method. [Pg.137]

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