浅层无压含水层瞬态地下水位的数值建模:双曲理论和均衡有限体积方案

IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES
Ying-Hsin Wu, Eiichi Nakakita
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引用次数: 0

摘要

我们提出了一种能够模拟非承压含水层中地下水浅层岩相面瞬态运动的新方法。该方法建立在新的地下水位运动综合理论和相应的高效数值方案之上。在理论方面,我们根据非稳态达西定律推导出一套新的控制方程,由深度平均连续性方程和动量方程构成。推导出的控制方程属于双曲型,由于惯性运动的特征时间尺度比渗流运动的时间尺度相对较短,因此动量方程中存在僵化项。为了有效求解衍生的双曲系统,在数值方面,我们采用了 f 波传播算法,这是一种显式有限体积法,当动量快速松弛到稳态平衡时,可以确保数值收敛和平衡求解。通过将结果与地下水丘多维扩散经典问题的解析解进行比较,成功地进行了验证。这项研究表明,所提出的方法可以准确和令人满意地模拟非承压含水层中浅层地下水位的时空分布及其湿润前沿。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Numerical modeling of transient water table in shallow unconfined aquifers: A hyperbolic theory and well-balanced finite volume scheme
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.
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来源期刊
Advances in Water Resources
Advances in Water Resources 环境科学-水资源
CiteScore
9.40
自引率
6.40%
发文量
171
审稿时长
36 days
期刊介绍: Advances in Water Resources provides a forum for the presentation of fundamental scientific advances in the understanding of water resources systems. The scope of Advances in Water Resources includes any combination of theoretical, computational, and experimental approaches used to advance fundamental understanding of surface or subsurface water resources systems or the interaction of these systems with the atmosphere, geosphere, biosphere, and human societies. Manuscripts involving case studies that do not attempt to reach broader conclusions, research on engineering design, applied hydraulics, or water quality and treatment, as well as applications of existing knowledge that do not advance fundamental understanding of hydrological processes, are not appropriate for Advances in Water Resources. Examples of appropriate topical areas that will be considered include the following: • Surface and subsurface hydrology • Hydrometeorology • Environmental fluid dynamics • Ecohydrology and ecohydrodynamics • Multiphase transport phenomena in porous media • Fluid flow and species transport and reaction processes
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