British Geological Survey, Kingsley Dunham Centre, Keyworth, Nottinghamshire, UK.
Ground Water. 2013 Jan-Feb;51(1):66-75. doi: 10.1111/j.1745-6584.2012.00924.x. Epub 2012 Mar 12.
Grid refinement is introduced in a numerical groundwater model to increase the accuracy of the solution over local areas without compromising the run time of the model. Numerical methods developed for grid refinement suffered certain drawbacks, for example, deficiencies in the implemented interpolation technique; the non-reciprocity in head calculations or flow calculations; lack of accuracy resulting from high truncation errors, and numerical problems resulting from the construction of elongated meshes. A refinement scheme based on the divergence theorem and Taylor's expansions is presented in this article. This scheme is based on the work of De Marsily (1986) but includes more terms of the Taylor's series to improve the numerical solution. In this scheme, flow reciprocity is maintained and high order of refinement was achievable. The new numerical method is applied to simulate groundwater flows in homogeneous and heterogeneous confined aquifers. It produced results with acceptable degrees of accuracy. This method shows the potential for its application to solving groundwater heads over nested meshes with irregular shapes.
网格细化被引入到一个数值地下水模型中，以提高局部地区解的准确性，而不会影响模型的运行时间。为网格细化开发的数值方法存在某些缺陷，例如，实施的插值技术存在缺陷；水头计算或流量计算的不可互易性；由于截断误差大而导致的精度不足，以及由于构建细长网格而导致的数值问题。本文提出了一种基于散度定理和泰勒展开式的细化方案。该方案基于德马尔斯利（De Marsily）（1986 年）的工作，但包括泰勒级数的更多项，以改进数值解。在该方案中，保持了流量互易性，并且可以实现高细化阶。新的数值方法被应用于模拟均质和非均质承压含水层中的地下水流动。它产生了具有可接受精度的结果。该方法显示了其在解决具有不规则形状的嵌套网格中的地下水水头问题上的应用潜力。
