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.

The interaction of a fibre tangle with an airflow

1967 ◽  
Vol 27 (3) ◽  
pp. 561-580 ◽  
Author(s):  
Paul A. Taub
Keyword(s):  
Unsteady Flow ◽  
Numerical Solution ◽  
Analytical Model ◽  
Method Of Characteristics ◽  
Solution Procedure ◽  
Governing Equations ◽  
Stress Strain ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Flow Configurations

An analytical model of the interaction of a fibre tangle with an airflow is proposed. This model replaces the discrete fibres by a continuum medium with a non-linear stress-strain law. The governing equations have been examined for one-dimensional unsteady flow configurations and have been found to possess five characteristic directions.A numerical-solution procedure, based upon the method of characteristics, has been outlined and applied to the flow within a dilation chamber. A fibre sample is located at the centre of the chamber, which is alternately pressurized and depressurized.

scholarly journals On the Numerical Solution of Fractional Hyperbolic Partial Differential Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Fadime Dal ◽  
Zehra Pinar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Hyperbolic Partial Differential Equations ◽  
Stability Estimates ◽  
Partial Differential ◽  
One Dimensional ◽  
Gauss Elimination ◽  
Gauss Elimination Method

The stable difference scheme for the numerical solution of the mixed problem for the multidimensional fractional hyperbolic equation is presented. Stability estimates for the solution of this difference scheme and for the first and second orders difference derivatives are obtained. A procedure of modified Gauss elimination method is used for solving this difference scheme in the case of one-dimensional fractional hyperbolic partial differential equations.

scholarly journals Numerical solution of advection-diffusion equation using finite difference schemes

2020 ◽  
Vol 55 (1) ◽  
pp. 15-22
Author(s):  
LS Andallah ◽  
MR Khatun
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Finite Difference Schemes ◽  
Qualitative Behavior ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Nicolson Scheme ◽  
And Diffusion ◽  
Crank Nicolson

This paper presents numerical simulation of one-dimensional advection-diffusion equation. We study the analytical solution of advection diffusion equation as an initial value problem in infinite space and realize the qualitative behavior of the solution in terms of advection and diffusion co-efficient. We obtain the numerical solution of this equation by using explicit centered difference scheme and Crank-Nicolson scheme for prescribed initial and boundary data. We implement the numerical scheme by developing a computer programming code and present the stability analysis of Crank-Nicolson scheme for ADE. For the validity test, we perform error estimation of the numerical scheme and presented the numerical features of rate of convergence graphically. The qualitative behavior of the ADE for different choice of the advection and diffusion co-efficient is verified. Finally, we estimate the pollutant in a river at different times and different points by using these numerical scheme. Bangladesh J. Sci. Ind. Res.55(1), 15-22, 2020

scholarly journals Approximating the Solution Stochastic Process of the Random Cauchy One-Dimensional Heat Model

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
A. Navarro-Quiles ◽  
J.-V. Romero ◽  
M.-D. Roselló ◽  
M. A. Sohaly
Keyword(s):  
Stochastic Process ◽  
Standard Deviation ◽  
Finite Difference ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Sufficient Conditions ◽  
Numerical Approximations ◽  
One Dimensional ◽  
The Mean ◽  
Theoretical Results

This paper deals with the numerical solution of the random Cauchy one-dimensional heat model. We propose a random finite difference numerical scheme to construct numerical approximations to the solution stochastic process. We establish sufficient conditions in order to guarantee the consistency and stability of the proposed random numerical scheme. The theoretical results are illustrated by means of an example where reliable approximations of the mean and standard deviation to the solution stochastic process are given.

scholarly journals On the numerical solution of the one-dimensional convection-diffusion equation

2005 ◽  
Vol 2005 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Numerical Solution ◽  
Partial Differential ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The One

The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes several finite difference schemes for solving the one-dimensional convection-diffusion equation with constant coefficients. In this research the use of modified equivalent partial differential equation (MEPDE) as a means of estimating the order of accuracy of a given finite difference technique is emphasized. This approach can unify the deduction of arbitrary techniques for the numerical solution of convection-diffusion equation. It is also used to develop new methods of high accuracy. This approach allows simple comparison of the errors associated with the partial differential equation. Various difference approximations are derived for the one-dimensional constant coefficient convection-diffusion equation. The results of a numerical experiment are provided, to verify the efficiency of the designed new algorithms. The paper ends with a concluding remark.

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