Solving the depth-integrated solute transport equation with a TVD-MacCormack scheme
Solving the depth-integrated solute transport equation with a TVD-MacCormack scheme
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DOI：
10.1016/j.envsoft.2010.06.008
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发表时间：
2010-12
期刊：
影响因子：
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通讯作者：
D. Liang;Xiaolin Wang;R. Falconer;B. Bockelmann-Evans
中科院分区：
文献类型：
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作者：
D. Liang;Xiaolin Wang;R. Falconer;B. Bockelmann-Evans
本文详细介绍了一个预测浅水沃茨中溶质运移的数值模型。交替算子分裂技术是用来分离的空间离散的平流和扩散项在每一步的时间推进过程。在扩散阶段，使用二阶精度中心格式。在平流阶段，五点总变差递减（TVD）的标准MacCormack方案的修改。通过比较数值预测与分析解决方案和其他一些数值模型的结果，理想化的测试用例的模型性能进行检查。该模型也被用来模拟污染物云在泰晤士河河口，广泛的润湿和干燥发生的潮汐振荡的运动。本模型在求解自然水环境中溶质运移问题时显示出足够高的效率和精度。它是免费的虚拟振荡接近尖锐的浓度梯度，同时保持二阶精度在光滑区域。还注意确保在复杂流动情况下准确处理交叉扩散项和质量平衡。
Details are given of a numerical model for predicting solute transport in shallow waters. The alternating operator-splitting technique is used to separate the spatial discretisation of the advection and diffusion terms in each step of the time marching procedure. In the diffusion stage, a second-order accurate central scheme is used. In the advection stage, a five-point Total Variation Diminishing (TVD) modification is made to the standard MacCormack scheme. The model performance is examined by comparing numerical predictions with analytical solutions and some other numerical model results for idealised test cases. The model is also used to simulate the motion of a contaminant cloud in the River Thames estuary, where extensive wetting and drying occurs with the tidal oscillation. The present model displays sufficiently high efficiency and accuracy in solving the solute transport problems in a natural aquatic environment. It is free of fictitious oscillations close to sharp concentration gradients, while retaining second-order accuracy in smooth regions. Attention has also been paid to ensure the accurate treatment of the cross-diffusion terms and mass balance in complex flow situations.