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首页> 外文期刊>Journal of Electroanalytical Chemistry: An International Journal Devoted to All Aspects of Electrode Kinetics, Interfacial Structure, Properties of Electrolytes, Colloid and Biological Electrochemistry >Digital simulations on unequally spaced grids. Part 2. Using the box method by discretisation on a transformed equally spaced grid
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Digital simulations on unequally spaced grids. Part 2. Using the box method by discretisation on a transformed equally spaced grid

机译：在不等距网格上的数字仿真。第2部分。在变换后的等距网格上通过离散化使用盒方法

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The paper demonstrates that using the box method on a transformed equally spaced grid can be accomplished in such a way that the integral flux conservation property of the exact equations will be preserved by the discretised ones. That means, when executing simulations on an exponentially expanding grid, the computed flux becomes virtually independent of grid expansion. Unlike the point of finite element method where the entire concentration profiles must be refined to ensure the accuracy of the simulate flux, the error obtained by the box method can be controlled simply by moving the first concentration point closer and closer to the electrode. This can be done with the smallest possible number of grid points even on strongly expanding grids without affecting the accuracy of the flux computation provided the grid expansion factor ΔY remains ≤0.5. The mathematical explanation of the flux conservation property given here for a simple diffusion problem will be extended in subsequent papers to more relevant systems involving chemical reactions coupled with the charge transfer processes.
机译：本文证明，在变换后的等距网格上使用盒方法可以实现这种方式，即精确方程的积分通量守恒性质将由离散方程保留。这意味着，在对指数扩展的网格执行仿真时，计算出的通量实际上变得与网格扩展无关。不像有限元法中必须完善整个浓度分布图以确保模拟通量的精度那样，通过盒式方法获得的误差可以简单地通过使第一个浓度点越来越靠近电极来控制。只要网格扩展因子ΔY保持≤0.5，即使在强扩展的网格上，也可以使用尽可能少的网格点数完成此操作，而不会影响通量计算的准确性。此处给出的关于简单扩散问题的通量守恒特性的数学解释将在随后的论文中扩展到涉及化学反应和电荷转移过程的更相关的系统。

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