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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 >Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations Part 6. Testing of the finite-difference patch-adaptive strategy on example models with solution difficulties at the electrodes, in one-dimensional spac
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Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations Part 6. Testing of the finite-difference patch-adaptive strategy on example models with solution difficulties at the electrodes, in one-dimensional spac

机译：动态自适应网格技术在电化学动力学方程式求解中的应用第6部分。在一维空间中，在电极上具有求解困难的示例模型上对有限差分贴片自适应策略的测试

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The patch-adaptive strategy described in Part 5 proves to provide correct, fairly efficient, and nearly automatic solutions to six representative example electrochemical kinetic models in one-dimensional space geometry, that exhibit difficult-to-resolve local spatial and temporal solution structures at the electrodes. The models describe: the square-wave controlled potential transient for an uncomplicated heterogeneous charge transfer reaction, the potential step method and linear potential sweep voltammetry for the standard catalytic reaction mechanism with a pseudo-first-order homogeneous reaction, linear potential sweep voltammetry for an EC reaction mechanism involving a follow-up homogeneous dimerisation, steady-state voltammetry at a rotating disc electrode, and steady-state voltammetry at a spherical microelectrode. These examples are characterised by extremely thin reaction layers and other instances of local spatial regions of considerable variations of the solution, including transient effects caused by temporal discontinuities of boundary conditions. The strategy creates dynamically spatio-temporal grids well adapted to such solution structures, without any a priori knowledge about their location. The accuracy of the numerical solutions proves well controlled by means of error tolerance parameters. Numerical difficulties observed with the previously described adaptive moving grid technique do not occur in the present strategy. However, further work is needed to improve the performance of the strategy in the cases of thin reaction layers associated with fast second-order homogeneous reactions, and boundary layers associated with hydrodynamic electroanalytical methods, for which the computational effort appears too large.
机译：第5部分中所述的贴片自适应策略证明可以为一维空间几何中的六个代表性示例电化学动力学模型提供正确，相当有效且几乎自动的解决方案，这些模型在模型中表现出难以解析的局部时空解决方案结构。电极。这些模型描述了：简单复杂的异质电荷转移反应的方波控制电势瞬变，标准催化反应机理与拟一阶均相反应的电势阶跃法和线性电势伏安法， EC反应机理包括后续的均相二聚化，转盘电极上的稳态伏安法和球形微电极上的稳态伏安法。这些示例的特点是反应层非常薄，溶液的其他局部空间区域变化很大，包括边界条件的时间不连续性引起的瞬态效应。该策略创建了非常适合此类解决方案结构的动态时空网格，而无需任何先验知识。数值解决方案的精度通过误差容限参数得到了很好的控制。用先前描述的自适应移动网格技术观察到的数值困难在本策略中不会发生。但是，在与快速二阶均相反应相关的薄反应层和与流体动力电分析方法相关的边界层的情况下，需要进行进一步的工作来提高该策略的性能，因为对于这些计算而言，计算工作显得太大了。

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