地下水水流与污染物迁移数值模型开发及应用研究

地下水水流与污染物迁移数值模型是研究地下水污染物迁移的重要手段，对地下水资源管理和污染防治具有指导作用。然而，在地下水模型应用中，由于含水层空间的复杂性，以及地表水-地下水耦合模拟的需要，地下水模型的适用性遇到了更大的挑战。发展空间适应性更强、耦合应用性更高的地下水数值模型对推动地下水、地下水-地表水资源和环境的管理具有重要的意义。基于此，本文针对含水层在水平与垂向上空间尺度的差异性以及地表水-地下水耦合模拟的需求，发展并开发了两种地下水水流与污染物迁移数值模型：（1）基于有限元与有限差分耦合的地下水水流与污染物迁移模型（FE-FDM）；（2）基于任意多边形网格剖分的地下水水流与污染物迁移模型（APFVM）。

论文对饱和-非饱和地下水水流与污染物迁移控制方程，在水平方向采用有限元法离散，在竖直方向采用有限差分法离散，推导得到数值离散格式，由此建立基于FE-FDM的地下水水流与污染物迁移模型，利用该模型模拟典型算例地下水水流与污染物迁移过程，通过与解析解、通用软件模拟结果进行对比，验证模型的准确性，并将其应用到垃圾填埋场地下水污染物迁移模拟研究之中。结果表明：（1）基于FE-FDM的地下水水流模型在4个典型算例的计算结果，均与解析解和通用软件计算结果有良好的一致性，说明该模型能够准确模拟饱和-非饱和水流运动规律；（2）基于FE-FDM的地下水污染物迁移数值模型在3个典型算例的模拟结果，均与常用软件的计算结果有良好的一致性，说明该模型能够准确模拟地下水污染物迁移规律；（3）某垃圾填埋场地下水污染物迁移模拟研究表明，基于FE-FDM的地下水水流与污染物迁移模型可有效应用到实际案例中，对垃圾填埋场污染物迁移规律研究及防治可起到重要技术支撑作用；（4）基于FE-FDM的地下水模型结合了有限元法边界适应性强和有限差分法计算简洁等优势，提高了模型对不规则含水系统空间的适应性。

为进一步提高地下水模型网格剖分的灵活性及耦合应用能力，论文基于有限体积法（FVM），对饱和地下水水流与污染物迁移控制方程在水平方向利用多点通量近似方法进行离散，在竖直方向采用两点近似方法进行离散，推导得到数值离散格式，由此建立基于APFVM的地下水水流与污染物迁移模型。通过典型算例验证新模型的准确性，并将其应用到平谷盆地地下水污染物迁移模拟研究之中。结果表明：（1）基于APFVM的地下水水流模型在5个典型算例的计算结果，均与解析解和常用软件的计算结果有良好的一致性，说明该模型能够准确模拟地下水水流运动规律；（2）基于APFVM的地下水污染物迁移模型在5个典型算例的计算结果，均与常用软件的计算结果有良好的一致性，说明该模型能够准确模拟地下水污染物迁移规律；（3）平谷盆地污染物迁移模拟应用表明，基于APFVM的地下水水流与污染物迁移模型可有效应用到实际案例中，对地下水污染物迁移规律研究及防治可起到重要技术支撑作用；（4）基于APFVM的地下水模型可应用于任意多边形网格剖分的地下水模拟中，极大地提高了地下水数值模拟网格剖分的灵活性及其耦合应用能力。

本文通过两种地下水模型（FE-FDM、APFVM）研究，将有限元、有限差分计算方法耦合在一起，并引入任意多边形网格剖分计算方法，提高了地下水模型空间剖分灵活性和对不规则含水层系统的适应性，拓展了地下水计算模型和理论；基于任意多边形网格的地下水水流与污染物迁移模型，可采用子流域为网格单元进行建模，为实现以子流域为统一网格单元的地表水-地下水耦合计算与应用奠定基础，对地表水-地下水污染协同防治具有重要意义。

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