scholarly journals Fuzzy Solution to the Unconfined Aquifer Problem

Water ◽  
2018 ◽  
Vol 11 (1) ◽  
pp. 54 ◽  
Author(s):  
Christos Tzimopoulos ◽  
Kyriakos Papadopoulos ◽  
Christos Evangelides ◽  
Basil Papadopoulos
Keyword(s):  
Boussinesq Equation ◽  
Water Movement ◽  
Unconfined Aquifer ◽  
Water Volume ◽  
Irrigation Projects ◽  
Sudden Rise ◽  
Fuzzy Solution ◽  
Uncertainty Level ◽  
Subsequent Stabilization ◽  
Water Profile

In this article, the solution to the fuzzy second order unsteady partial differential equation (Boussinesq equation) is examined, for the case of an aquifer recharging from a lake. In the examined problem, there is a sudden rise and subsequent stabilization of the lake’s water level, thus the aquifer is recharging from the lake. The aquifer boundary conditions are fuzzy and create ambiguities to the solution of the problem. Since the aforementioned problem concerns differential equations, the generalized Hukuhara (gH) derivative was used for total derivatives, as well as the extension of this theory concerning partial derivatives. The case studies proved to follow the generalized Hukuhara (gH) derivative conditions and they offer a unique solution. The development of the aquifer water profile was examined, as well as the calculation of the recharging fuzzy water movement profiles, velocity, and volume, and the results were depicted in diagrams. According to presented results, the hydraulic engineer, being specialist in irrigation projects or in water management, could estimate the appropriate water volume quantity with an uncertainty level, given by the α-cuts.

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.

scholarly journals Ski piste snow ablation versus potential infiltration (Veporic Unit, Western Carpathians)

2020 ◽  
Vol 68 (1) ◽  
pp. 28-37 ◽  
Author(s):  
Michal Mikloš ◽  
Dušan Igaz ◽  
Karol Šinka ◽  
Jana Škvareninová ◽  
Martin Jančo ◽  
...  
Keyword(s):  
Snow Water Equivalent ◽  
Water Movement ◽  
Average Rate ◽  
High Volume ◽  
Ablation Rate ◽  
Frozen Soil ◽  
Western Carpathians ◽  
Water Volume ◽  
South Central ◽  
Natural Snow

AbstractSnow production results in high volume of snow that is remaining on the low-elevation ski pistes after snowmelt of natural snow on the off-piste sites. The aim of this study was to identify snow/ice depth, snow density, and snow water equivalent of remaining ski piste snowpack to calculate and to compare snow ablation water volume with potential infiltration on the ski piste area at South-Central Slovak ski center Košútka (Inner Western Carpathians; temperate zone). Snow ablation water volume was calculated from manual snow depth and density measurements, which were performed at the end of five winter seasons 2010–2011 to 2015–2016, except for season 2013–2014. The laser diffraction analyzes were carried out to identify soil grain size and subsequently the hydraulic conductivity of soil to calculate the infiltration. The average rate of water movement through soil was seven times as high as five seasons’ average ablation rate of ski piste snowpack; nevertheless, the ski piste area was potentially able to infiltrate only 47% of snow ablation water volume on average. Limitation for infiltration was frozen soil and ice layers below the ski piste snowpack and low snow-free area at the beginning of the studied ablation period.

scholarly journals Fuzzy numerical solution to the unconfined aquifer problem under the Boussinesq equation

2021 ◽  
Author(s):  
N. Samarinas ◽  
C. Tzimopoulos ◽  
C. Evangelides
Keyword(s):  
Unsteady Flow ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Boussinesq Equation ◽  
Unconfined Aquifer ◽  
Physical Problem ◽  
Soil Parameters ◽  
Partial Differential ◽  
One Dimensional ◽  
Nicolson Scheme

Abstract In this article, the fuzzy numerical solution of the linearized one dimensional Boussinesq equation of unsteady flow in a semi-infinite unconfined aquifer bordering a lake is examined. The equation describing the problem is a partial differential parabolic equation of second order. This equation requires the knowledge of the initial and boundary conditions as well as the various soil parameters. The above auxiliary conditions are subject to different kinds of uncertainty due to human and machine imprecision and create ambiguities to the solution of the problem and a fuzzy method is introduced. Since the physical problem refers to a partial differential equation, the generalized Hukuhara (gH) derivative was used, as well as the extension of this theory regarding the partial derivatives. The objective of this paper is to compare the fuzzy numerical and analytical results, for two different cases of physical problem of aquifer's unsteady flow, in order to prove the reliability and efficiency of the proposed fuzzy numerical scheme (fuzzy Crank-Nicolson scheme). The comparison of the methods was based on the transformed Haussdorf metric, presented that the distances between the analytical and numerical results tend to zero.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

Fuzzy Sets Theory in Comparison with Stochastic Methods to Analyse Nonlinear Behaviour of a Steel Member under Compression

2005 ◽  
Vol 10 (1) ◽  
pp. 65-75 ◽  
Author(s):  
Z. Kala
Keyword(s):  
Fuzzy Sets ◽  
Carrying Capacity ◽  
Stochastic Methods ◽  
Nonlinear Behaviour ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Input Parameters ◽  
Stochastic Solution ◽  
Fuzzy Solution ◽  
Sets Theory

The load-carrying capacity of the member with imperfections under axial compression is analysed in the present paper. The study is divided into two parts: (i) in the first one, the input parameters are considered to be random numbers (with distribution of probability functions obtained from experimental results and/or tolerance standard), while (ii) in the other one, the input parameters are considered to be fuzzy numbers (with membership functions). The load-carrying capacity was calculated by geometrical nonlinear solution of a beam by means of the finite element method. In the case (ii), the membership function was determined by applying the fuzzy sets, whereas in the case (i), the distribution probability function of load-carrying capacity was determined. For (i) stochastic solution, the numerical simulation Monte Carlo method was applied, whereas for (ii) fuzzy solution, the method of the so-called α cuts was applied. The design load-carrying capacity was determined according to the EC3 and EN1990 standards. The results of the fuzzy, stochastic and deterministic analyses are compared in the concluding part of the paper.

Aqueous Phase Diffusion in Crystalline Rock

1981 ◽  
Vol 11 ◽  
Author(s):  
M.H. Bradbury ◽  
D. Lever ◽  
D. Kinsey
Keyword(s):  
Radioactive Waste ◽  
Aqueous Phase ◽  
Water Movement ◽  
Degradation Products ◽  
Crystalline Rock ◽  
Crystalline Rocks ◽  
Radionuclide Transport ◽  
Fracture Networks ◽  
Phase Diffusion ◽  
Main Factors

One of the options being considered for the disposal of radioactive waste is deep burial in crystalline rocks such as granite. It is generally recognised that in such rocks groundwater flows mainly through the fracture networks so that these will be the “highways” for the return of radionuclides to the biosphere. The main factors retarding the radionuclide transport have been considered to be the slow water movement in the fissures over the long distances involved together with sorption both in man-made barriers surrounding the waste, and onto rock surfaces and degradation products in the fissures.

Sign in / Sign up

Export Citation Format

Share Document