scholarly journals Evaluation of hillslope storage with variable width under temporally varied rainfall recharge

2021 ◽  
Author(s):  
Ping-Cheng Hsieh ◽  
Tzu-Ting Huang
Keyword(s):  
Groundwater Flow ◽  
Analytical Solutions ◽  
Water Conservation ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Time Discretization ◽  
Third Order ◽  
Analytical And Numerical Solutions ◽  
Rainfall Recharge ◽  
Integral Transform Technique

Abstract. This study discussed water storage in aquifers of hillslopes under temporally varied rainfall recharge by employing a hillslope-storage equation to simulate groundwater flow. The hillslope width was assumed to vary exponentially to denote the following complex hillslope types: uniform, convergent, and divergent. Both analytical and numerical solutions were acquired for the storage equation with a recharge source. The analytical solution was obtained using an integral transform technique. The numerical solution was obtained using a finite difference method in which the upwind scheme was used for space derivatives and the third-order Runge–Kutta scheme was used for time discretization. The results revealed that hillslope type significantly influences the drains of hillslope storage. Drainage was the fastest for divergent hillslopes and the slowest for convergent hillslopes. The results obtained from analytical solutions require the tuning of a fitting parameter to better describe the groundwater flow. However, a gap existed between the analytical and numerical solutions under the same scenario owing to the different versions of the hillslope-storage equation. The study findings implied that numerical solutions are superior to analytical solutions for the nonlinear hillslope-storage equation, whereas the analytical solutions are better for the linearized hillslope-storage equation. The findings thus can benefit research on and have application in soil and water conservation.

Analytical solution for heat and moisture diffusion in layered materials

2010 ◽  
Vol 47 (6) ◽  
pp. 595-608 ◽  
Author(s):  
Jeongwoo Lee ◽  
Ji-Tae Kim ◽  
Il-Moon Chung ◽  
Nam Won Kim
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Moisture Diffusion ◽  
Layered Materials ◽  
Diffusion Problem ◽  
Moisture Distribution ◽  
Coupled Flow ◽  
Coupled Diffusion ◽  
Heat And Moisture

The study of heat and moisture flows in multiple layers of different materials that make up the unsaturated zone is of great importance when characterizing the behaviour of these materials. In the present paper, analytical solutions of the one-dimensional heat and moisture coupled diffusion problem for layered materials under two different sets of boundary conditions are proposed. The coupled flow of heat and moisture are assumed to follow the theory of Philip and De Vries, and the solutions are derived analytically using integral transform methods. A comparison between the analytical and numerical solutions for one example problem shows satisfactory results. Furthermore, a procedure is presented for estimating heat and moisture distribution profiles in any layered materials using the derived analytical solutions. It is expected that the proposed analytical solutions will be used effectively for preliminary analyses of coupled heat and moisture movements in unsaturated porous media.

scholarly journals Response of Groundwater Levels in a Coastal Aquifer to Tidal Waves and Rainfall Recharge

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 625
Author(s):  
Ping-Cheng Hsieh ◽  
Jing-Lun Huang ◽  
Ming-Chang Wu
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Groundwater Level ◽  
Integral Transform ◽  
Decay Length ◽  
Groundwater Levels ◽  
Tidal Waves ◽  
New Finding ◽  
Rainfall Recharge ◽  
Integral Transform Technique

Groundwater level in coastal aquifers is usually affected by tidal waves and rainfall recharge. Therefore, the objective of this study is to present a mathematical model to account for the effects of tidal waves and rainfall recharge simultaneously. The model is based on the Dupuit–Forchheimer assumptions and is separated into a tidal waves component and rainfall recharge component. A new more general analytical solution for the recharge component is acquired by the generalized integral transform technique. The beach slope, the inclination of an impermeable base of an aquifer, and any randomly distributed rainfall recharge are taken into account in the model. A new finding is that the highest fluctuation in groundwater levels might occur when the range of rainfall recharge is larger than the decay length.

scholarly journals A parsimonious analytical model for simulating multispecies plume migration

2015 ◽  
Vol 12 (9) ◽  
pp. 8675-8726
Author(s):  
J.-S. Chen ◽  
C.-P. Liang ◽  
C.-W. Liu ◽  
L. Y. Li
Keyword(s):  
Analytical Model ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Chlorinated Solvents ◽  
Equation System ◽  
Screening Tools ◽  
Algebraic Equations ◽  
Fourier Cosine ◽  
Linear Algebraic Equations

Abstract. A parsimonious analytical model for rapidly predicting the long-term plume behavior of decaying contaminant such as radionuclide and dissolved chlorinated solvent is presented in this study. Generalized analytical solutions in compact format are derived for the two-dimensional advection-dispersion equations coupled with sequential first-order decay reactions involving an arbitrary number of species in groundwater system. The solution techniques involve the sequential applications of the Laplace, finite Fourier cosine, and generalized integral transforms to reduce the coupled partial differential equation system to a set of linear algebraic equations. The system of algebraic equations is next solved for each species in the transformed domain, and the solutions in the original domain are then obtained through consecutive integral transform inversions. Explicit form solutions for a special case are derived using the generalized analytical solutions and are verified against the numerical solutions. The analytical results indicate that the parsimonious analytical solutions are robust and accurate. The solutions are useful for serving as simulation or screening tools for assessing plume behaviors of decaying contaminants including the radionuclides and dissolved chlorinated solvents in groundwater systems.

Analytical and Numerical Solutions of the Riccati Equation Using the Method of Variation of Parameters. Application to Population Dynamics

2020 ◽  
Vol 15 (10) ◽  
Author(s):  
Orestes Tumbarell Aranda ◽  
Fernando A. Oliveira
Keyword(s):  
Population Dynamics ◽  
Pattern Formation ◽  
Riccati Equation ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Original Equation ◽  
Analytical And Numerical Solutions ◽  
Variation Of Parameters ◽  
Approximate Analytical Solutions ◽  
Independent Variable

Abstract This work presents new approximate analytical solutions for the Riccati equation (RE) resulting from the application of the method of variation of parameters. The original equation is solved using another RE explicitly dependent on the independent variable. The solutions obtained are easy to implement and highly applicable, which is confirmed by solving several examples corresponding to REs whose solution is known, as well as optimizing the method to determine the density of the members that make up a population. In this way, new perspectives are open in the study of the phenomenon of pattern formation.

scholarly journals An analytical model for simulating two-dimensional multispecies plume migration

2016 ◽  
Vol 20 (2) ◽  
pp. 733-753 ◽  
Author(s):  
Jui-Sheng Chen ◽  
Ching-Ping Liang ◽  
Chen-Wuing Liu ◽  
Loretta Y. Li
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Equation System ◽  
Screening Tools ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Fourier Cosine ◽  
Advection Dispersion ◽  
Linear Algebraic Equations

Abstract. The two-dimensional advection-dispersion equations coupled with sequential first-order decay reactions involving arbitrary number of species in groundwater system is considered to predict the two-dimensional plume behavior of decaying contaminant such as radionuclide and dissolved chlorinated solvent. Generalized analytical solutions in compact format are derived through the sequential application of the Laplace, finite Fourier cosine, and generalized integral transform to reduce the coupled partial differential equation system to a set of linear algebraic equations. The system of algebraic equations is next solved for each species in the transformed domain, and the solutions in the original domain are then obtained through consecutive integral transform inversions. Explicit form solutions for a special case are derived using the generalized analytical solutions and are compared with the numerical solutions. The analytical results indicate that the analytical solutions are robust, accurate and useful for simulation or screening tools to assess plume behaviors of decaying contaminants.

scholarly journals Uncertainty of volume fraction in bimrock using the scan-line method and its application in the estimation of deformability parameters

2019 ◽  
Vol 79 (4) ◽  
pp. 1651-1668
Author(s):  
Yu-Chen Lu ◽  
Yong-Ming Tien ◽  
Charng Hsein Juang ◽  
Jeen-Shang Lin
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Experimental Tests ◽  
Element Model ◽  
Engineering Properties ◽  
Line Method ◽  
Analytical And Numerical Solutions ◽  
Physical Tests ◽  
Scan Line

AbstractThe volume fraction within a bimrock or bimsoil is an essential parameter that is useful for estimating the engineering properties of heterogeneous geomaterials. This paper presents analytical and numerical solutions to quantify the uncertainty of volume fraction measurements in bimrock/bimsoil using a scan-line method. The analytical solutions for the mean and variance of volume fraction estimates are based on a representative volume element model. The numerical solution is obtained through simulations of scan-line measurements. This work also employs physical tests using CT scan images from artificial bimrock/bimsoil to validate these solutions. The results demonstrate that the uncertainties of the volume fraction depend on the magnitude of the volume fraction of the blocks, the diameter of the blocks, and the length of the scan line. The proposed analytical and numerical solutions are compared with existing physical experimental tests and analytical solutions. An illustrative example to demonstrate the estimation of the uncertainty of volume fraction using the scan-line measurement is present. Finally, an example application of the volume fraction characterization in the geological engineering, in terms of Young’s modulus estimation and characterization, is provided.

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