A metahillslope model based on an analytical solution to a linearized Boussinesq equation for temporally variable recharge rates

2002 ◽  
Vol 38 (12) ◽  
pp. 33-1-33-14 ◽  
Author(s):  
Valentijn R. N. Pauwels ◽  
Niko E. C. Verhoest ◽  
François P. De Troch
Keyword(s):  
Analytical Solution ◽  
Boussinesq Equation ◽  
Model Based ◽  
Linearized Boussinesq Equation ◽  
Recharge Rates

scholarly journals Variation of Groundwater Flow Caused by Any Spatiotemporally Varied Recharge

Water ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 287
Author(s):  
Ming-Chang Wu ◽  
Ping-Cheng Hsieh
Keyword(s):  
Analytical Solution ◽  
Groundwater Flow ◽  
Unconfined Aquifer ◽  
Initial Water ◽  
The Past ◽  
Sloping Aquifer ◽  
Taichung City ◽  
Spatially Distributed ◽  
Recharge Rates ◽  
Rainfall Recharge

The objective of this study was to develop a complete analytical solution to determining the effect of any varying rainfall recharge rates on groundwater flow in an unconfined sloping aquifer. The domain of the unconfined aquifer was assumed to be semi-infinite with an impervious bottom base, and the initial water level was parallel to the impervious bottom of a mild slope. In the past, similar problems have been discussed mostly by considering a uniform or temporally varying recharge rate, but the current study explored the variation of groundwater flow under temporally and spatially distributed recharge rates. The presented analytical solution was verified by comparing its results with those of previous research, and the practicability of the analytical solution was validated using the 2012 and 2013 data of a groundwater station in Dali District of Taichung City, Taiwan.

scholarly journals Improved Solutions to the Linearized Boussinesq Equation with Temporally Varied Rainfall Recharge for a Sloping Aquifer

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 826 ◽  
Author(s):  
Wu ◽  
Hsieh
Keyword(s):  
Groundwater Level ◽  
Boussinesq Equation ◽  
Integral Transformation ◽  
Transformation Method ◽  
Unconfined Aquifer ◽  
Convergence Criterion ◽  
Unconfined Aquifers ◽  
Linearized Boussinesq Equation ◽  
Sloping Aquifer ◽  
Rainfall Recharge

Sloping unconfined aquifers are commonly seen and well investigated in the literature. In this study, we propose a generalized integral transformation method to solve the linearized Boussinesq equation that governs the groundwater level in a sloping unconfined aquifer with an impermeable bottom. The groundwater level responses of this unconfined aquifer under temporally uniform recharge or nonuniform recharge events are discussed. After comparing with a numerical solution to the nonlinear Boussinesq equation, the proposed solution appears better than that proposed in a previous study. Besides, we found that the proposed solutions reached the convergence criterion much faster than the Laplace transform solution did. Moreover, the application of the proposed solution to temporally changing rainfall recharge is also proposed to improve on the previous quasi-steady state treatment of an unsteady recharge rate.

Analytical Solutions to the Linearized Boussinesq Equation for Assessing the Effects of Recharge on Aquifer Discharge1

2010 ◽  
Vol 46 (6) ◽  
pp. 1116-1132 ◽  
Author(s):  
Kevin G. Boggs ◽  
Robert W. Van Kirk ◽  
Gary S. Johnson ◽  
Jerry P. Fairley ◽  
P. Steve Porter
Keyword(s):  
Analytical Solutions ◽  
Boussinesq Equation ◽  
Linearized Boussinesq Equation

scholarly journals Analytical Solution of a New SEIR Model Based on Latent Period-Infectious Period Chronological Order

2021 ◽  
Author(s):  
Xiaoping Liu
Keyword(s):  
Analytical Solution ◽  
Latent Period ◽  
Infectious Period ◽  
Chronological Order ◽  
Underlying Assumption ◽  
Seir Model ◽  
Model Based ◽  
Exposed Individual ◽  
Line Passing ◽  
Model Equations

The Susceptible-Infectious-Recovered (SIR) and SIR derived epidemic models have been commonly used to analyze the spread of infectious diseases. The underlying assumption in these models, such as Susceptible-Exposed-Infectious-Recovered (SEIR) model, is that the change in variables E, I or R at time t is dependent on a fraction of E and I at time t. This means that after exposed on a day, this individual may become contagious or even recover on the same day. However, the real situation is different: an exposed individual will become infectious after a latent period (l) and then recover after an infectious period (i). In this study, we proposed a new SEIR model based on the latent period-infectious period chronological order (Liu X., Results Phys. 2021; 20:103712). An analytical solution to equations of this new SEIR model was derived. From this new SEIR model, we obtained a propagated curve of infectious cases under conditions l>i. Similar propagated epidemic curves were reported in literature. However, the conventional SEIR model failed to simulate the propagated epidemic curves under the same conditions. For l<i, the new SEIR models generated bell-shaped curves for infectious cases, and the curve is near symmetrical to the vertical line passing the curve peak. This characteristic can be found in many epidemic curves of daily COVID-19 cases reported from different countries. However, the curve generated from the conventional SEIR model is a right-skewed bell-shaped curve. An example for applying the analytical solution of the new SEIR model equations to simulate the reported daily COVID-19 cases was also given in this paper.

Sign in / Sign up

Export Citation Format

Share Document