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

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 req...

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Autores principales:	N. Samarinas, C. Tzimopoulos, C. Evangelides
Formato:	article
Lenguaje:	EN
Publicado:	IWA Publishing 2021
Materias:	boussinesq equation depth profiles fuzzy finite difference fuzzy partial differential equation gh-derivative Water supply for domestic and industrial purposes TD201-500 River, lake, and water-supply engineering (General) TC401-506
Acceso en línea:	https://doaj.org/article/f21ba68bae064667b87dcfc7300aee45
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spelling	oai:doaj.org-article:f21ba68bae064667b87dcfc7300aee452021-11-06T10:08:57ZFuzzy numerical solution to the unconfined aquifer problem under the Boussinesq equation1606-97491607-079810.2166/ws.2021.115https://doaj.org/article/f21ba68bae064667b87dcfc7300aee452021-09-01T00:00:00Zhttp://ws.iwaponline.com/content/21/6/3210https://doaj.org/toc/1606-9749https://doaj.org/toc/1607-0798In 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 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 for 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 is used, as well as the extension of this theory regarding partial derivatives. The objective of this paper is to compare the fuzzy numerical and analytical results, for two different cases of the physical problem of an 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 is based on the transformed Haussdorff metric, which shows that the distances between the analytical and numerical results tend to zero. HIGHLIGHTS Novel fuzzy numerical scheme.; Solve the Boussinesq equation in a fuzzy environment.; Compare the fuzzy scheme with the corresponding analytical results.; Include the uncertainties of the physical problem.; Provides a strong advantage to decision makers for efficient water management planning.;N. SamarinasC. TzimopoulosC. EvangelidesIWA Publishingarticleboussinesq equationdepth profilesfuzzy finite differencefuzzy partial differential equationgh-derivativeWater supply for domestic and industrial purposesTD201-500River, lake, and water-supply engineering (General)TC401-506ENWater Supply, Vol 21, Iss 6, Pp 3210-3224 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	boussinesq equation depth profiles fuzzy finite difference fuzzy partial differential equation gh-derivative Water supply for domestic and industrial purposes TD201-500 River, lake, and water-supply engineering (General) TC401-506
spellingShingle	boussinesq equation depth profiles fuzzy finite difference fuzzy partial differential equation gh-derivative Water supply for domestic and industrial purposes TD201-500 River, lake, and water-supply engineering (General) TC401-506 N. Samarinas C. Tzimopoulos C. Evangelides Fuzzy numerical solution to the unconfined aquifer problem under the Boussinesq equation
description	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 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 for 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 is used, as well as the extension of this theory regarding partial derivatives. The objective of this paper is to compare the fuzzy numerical and analytical results, for two different cases of the physical problem of an 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 is based on the transformed Haussdorff metric, which shows that the distances between the analytical and numerical results tend to zero. HIGHLIGHTS Novel fuzzy numerical scheme.; Solve the Boussinesq equation in a fuzzy environment.; Compare the fuzzy scheme with the corresponding analytical results.; Include the uncertainties of the physical problem.; Provides a strong advantage to decision makers for efficient water management planning.;
format	article
author	N. Samarinas C. Tzimopoulos C. Evangelides
author_facet	N. Samarinas C. Tzimopoulos C. Evangelides
author_sort	N. Samarinas
title	Fuzzy numerical solution to the unconfined aquifer problem under the Boussinesq equation
title_short	Fuzzy numerical solution to the unconfined aquifer problem under the Boussinesq equation
title_full	Fuzzy numerical solution to the unconfined aquifer problem under the Boussinesq equation
title_fullStr	Fuzzy numerical solution to the unconfined aquifer problem under the Boussinesq equation
title_full_unstemmed	Fuzzy numerical solution to the unconfined aquifer problem under the Boussinesq equation
title_sort	fuzzy numerical solution to the unconfined aquifer problem under the boussinesq equation
publisher	IWA Publishing
publishDate	2021
url	https://doaj.org/article/f21ba68bae064667b87dcfc7300aee45
work_keys_str_mv	AT nsamarinas fuzzynumericalsolutiontotheunconfinedaquiferproblemundertheboussinesqequation AT ctzimopoulos fuzzynumericalsolutiontotheunconfinedaquiferproblemundertheboussinesqequation AT cevangelides fuzzynumericalsolutiontotheunconfinedaquiferproblemundertheboussinesqequation
_version_	1718443830399729664

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

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