TY - JOUR
T1 - New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions
AU - Yeh, Hund-Der
AU - Chang, Ya Chi
PY - 2006/3
Y1 - 2006/3
N2 - The hydraulic head distribution in a wedge-shaped aquifer depends on the wedge angle and the topographic and hydrogeological boundary conditions. In addition, an equation in terms of the radial distance with trigonometric functions along the boundary may be suitable to describe the water level configuration for a valley flank with a gentle sloping and rolling topography. This paper develops a general mathematical model including the governing equation and a variety of boundary conditions for the groundwater flow within a wedge-shaped aquifer. Based on the model, a new closed-form solution for transient flow in the wedge-shaped aquifer is derived via the finite sine transform and Hankel transform. In addition, a numerical approach, including the roots search scheme, the Gaussian quadrature, and Shanks' method, is proposed for efficiently evaluating the infinite series and the infinite integral presented in the solution. This solution may be used to describe the head distribution for wedges that image theory is inapplicable, and to explore the effects of the recharge from various topographic boundaries on the groundwater flow system within a wedge-shaped aquifer.
AB - The hydraulic head distribution in a wedge-shaped aquifer depends on the wedge angle and the topographic and hydrogeological boundary conditions. In addition, an equation in terms of the radial distance with trigonometric functions along the boundary may be suitable to describe the water level configuration for a valley flank with a gentle sloping and rolling topography. This paper develops a general mathematical model including the governing equation and a variety of boundary conditions for the groundwater flow within a wedge-shaped aquifer. Based on the model, a new closed-form solution for transient flow in the wedge-shaped aquifer is derived via the finite sine transform and Hankel transform. In addition, a numerical approach, including the roots search scheme, the Gaussian quadrature, and Shanks' method, is proposed for efficiently evaluating the infinite series and the infinite integral presented in the solution. This solution may be used to describe the head distribution for wedges that image theory is inapplicable, and to explore the effects of the recharge from various topographic boundaries on the groundwater flow system within a wedge-shaped aquifer.
KW - Analytical solution
KW - Finite sine transform
KW - Groundwater
KW - Hankel transform
KW - Numerical approach
KW - Wedge-shaped aquifer
UR - http://www.scopus.com/inward/record.url?scp=29444440002&partnerID=8YFLogxK
U2 - 10.1016/j.advwatres.2005.06.002
DO - 10.1016/j.advwatres.2005.06.002
M3 - Article
AN - SCOPUS:29444440002
SN - 0309-1708
VL - 29
SP - 471
EP - 480
JO - Advances in Water Resources
JF - Advances in Water Resources
IS - 3
ER -