We present a new methodology capable of modeling transient motion of shallow phreatic surface of groundwater in unconfined aquifers. This methodology is founded on a new and comprehensive theory for water table motion and a corresponding efficient numerical scheme. In the theoretical aspect, we derived a new set of governing equations constituted by a depth-averaged continuity equation and momentum equations based on unsteady Darcy’s law. The derived governing equations are of the hyperbolic type and possess stiff terms in the momentum equations due to the inertia motion in a characteristic time scale that is relatively shorter than the time scale of seepage motion. To effectively solve the derived hyperbolic system with stiff terms, in the numerical aspect, we utilize f-wave propagation algorithm, an explicit finite volume method, that can ensure numerical convergence and well-balancing solutions when momentum is rapidly relaxing to an equilibrium of steady state. Verification is successfully performed by comparing the results with analytic solutions to the classic problem of multidimensional spreading of a groundwater mound. This study demonstrates that the proposed methodology can accurately and satisfactorily simulate the spatiotemporal distribution of shallow water table and its wetting front in unconfined aquifers.

中文翻译：

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浅层非承压含水层瞬态地下水位的数值模拟：双曲理论与均衡有限体积方案


我们提出了一种新方法，能够模拟非承压含水层中地下水浅层表面的瞬态运动。该方法建立在一种新的综合地下水位运动理论和相应的高效数值方案之上。在理论方面，我们推导出了一组新的控制方程，这些方程由基于非定常达西定律的深度平均连续性方程和动量方程组成。推导的控制方程是双曲类型的，由于惯性运动在特征时间尺度上相对短于渗流运动的时间尺度，因此在动量方程中具有刚性项。为了有效地求解具有刚性项的推导双曲系统，在数值方面，我们利用了 f 波传播算法，这是一种显式的有限体积方法，当动量迅速放松到稳态平衡时，可以确保数值收敛和均衡解。通过将结果与解析解与地下水丘多维扩展的经典问题进行比较，成功执行验证。本研究表明，所提出的方法能够准确、令人满意地模拟非承压含水层中浅水位及其润湿前沿的时空分布。