Tetra Tech GEO, Inc., Sterling, VA 20164, USA.
Ground Water. 2012 Nov-Dec;50(6):943-53. doi: 10.1111/j.1745-6584.2011.00905.x. Epub 2012 Jan 27.
Although based on exact analytical solutions, semi-analytical solute transport models can have significant numerical error in applications with high frequency oscillatory source terms and when parameter value combinations cause series solution approximations to converge slowly. Methods for correcting these numerical errors are presented and implemented in the AT123D code, which employs Green's functions to represent point, linear, and rectangular prismatic source zones. In order to increase its computational accuracy, a Romberg numerical integration scheme was added to AT123D with prespecified error criteria, variable time stepping, and partitioning of the integral to handle rapidly changing source terms. More rapidly converging series solution approximations for the Green's functions were also incorporated to improve both accuracy and computational efficiency for finite-depth aquifers. AT123D also has been modified to eliminate redundant calculations at points where approximate steady-state conditions have been reached to improve computational efficiency during numerical integration. These modifications help to decrease computer run times that can be excessive for three-dimensional problems with large numbers of computational points, small time steps, and/or long simulation time periods. Errors in the original AT123D code also were corrected in this modified version, AT123D-AT, in order to accurately simulate finite-duration (pulse) source releases.
虽然基于精确的解析解，但半解析溶质运移模型在高频振荡源项应用中可能会出现显著的数值误差，并且在参数值组合导致级数解逼近缓慢收敛时也是如此。本文提出了纠正这些数值误差的方法，并在 AT123D 代码中实现，该代码采用格林函数表示点源、线源和矩形棱柱形源区。为了提高其计算精度，在 AT123D 中添加了龙贝格数值积分方案，并规定了误差标准、可变时间步长和积分分区，以处理快速变化的源项。还采用了更快速收敛的级数解逼近格林函数，以提高有限深度含水层的计算精度和效率。AT123D 还进行了修改，以消除在达到近似稳态条件的点的冗余计算，从而在数值积分过程中提高计算效率。这些修改有助于减少计算机运行时间，对于具有大量计算点、小时间步长和/或长模拟时间段的三维问题，计算机运行时间可能会过长。在这个修改后的版本 AT123D-AT 中，还纠正了原始 AT123D 代码中的错误，以便准确模拟有限持续时间（脉冲）源释放。
