当前位置: X-MOL 学术J. Hydrol. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A Lattice Boltzmann model for 2D fractional advection-dispersion equation: Theory and application
Journal of Hydrology ( IF 6.4 ) Pub Date : 2018-09-01 , DOI: 10.1016/j.jhydrol.2018.06.083
Feng Wang , Xiaoxian Zhang , Xiaojun Shen , Jingsheng Sun

Abstract Natural soils and aquifers are inherently heterogenous and chemical transport through them is anomalous characterized by an early arrival followed by a persistent tail. How to describe such anomalous phenomena has been an interest and, as a result, a number of approaches have been proposed over the past few decades. Among others, the fractional advection-dispersion equation (FADE) is a model able to describe anomalous transport when the dispersion is regional rather than local as presumed in the classical advection-dispersion equation. Practical application of FADE needs numerical solutions, which is challenging because its spatial discretization gives rise to a full coefficient matrix. In this paper, we propose a Lattice Boltzmann model to solve the two-dimensional FADE. Given that the anomalous dispersion in soils and aquifers is hydrodynamic and caused by spatial variation in water velocity across the pore space and that the chemical plume spreads preferentially along the mean water-flow direction, the dispersion coefficient and the order of the fractional derivative should be both anisotropic. The anisotropies are solved by the two-relaxation time Lattice Boltzmann model using different relaxation parameters in different directions. Compared with existing numerical methods for the FADE, the proposed model has advantages that it is explicit, second-order accurate in both time and space, mass-conservative, and free of numerical dispersion; its stability is independent of dispersion coefficient. We verify the model against the analytical solution of a benchmark problem and then apply it to simulate Cl− movement in a tracer experiment conducted on an up-catchment hillslope. The results show that the FADE with backward skewness can reproduce the breakthrough curves measured from the experiment.

中文翻译:

二维分数阶对流-弥散方程的格子玻尔兹曼模型:理论与应用

摘要 天然土壤和含水层本质上是异质的,通过它们的化学物质运输是反常的,其特征是早到,然后是持续的拖尾。如何描述这种异常现象引起了人们的兴趣,因此在过去的几十年中提出了许多方法。其中,分数平流-弥散方程 (FADE) 是一种模型,当弥散是区域性的而不是经典对流-弥散方程中假定的局部时,该模型能够描述异常传输。FADE 的实际应用需要数值解,这是具有挑战性的,因为它的空间离散化会产生一个完整的系数矩阵。在本文中,我们提出了一个 Lattice Boltzmann 模型来解决二维 FADE。鉴于土壤和含水层中的异常弥散是水动力的,由穿过孔隙空间的水流速度的空间变化引起,并且化学羽流优先沿平均水流方向扩散,弥散系数和分数阶导数应为都是各向异性的。各向异性通过使用不同方向的不同弛豫参数的双弛豫时间格子 Boltzmann 模型求解。与现有的FADE数值方法相比,该模型具有显式、时空二阶精度、质量守恒、无数值色散等优点;其稳定性与色散系数无关。我们根据基准问题的解析解验证模型,然后将其应用于在上流山坡上进行的示踪实验中模拟 Cl- 运动。结果表明,具有后向偏度的 FADE 可以再现实验测量的突破曲线。
更新日期:2018-09-01
down
wechat
bug