scholarly journals A Short Review on Computational Hydraulics in the context of Water Resources Engineering

2021 ◽  
Author(s):  
Shiblu Sarker
Keyword(s):  
Water Resources ◽  
Differential Equations ◽  
Numerical Technique ◽  
Real Life ◽  
Short Review ◽  
Sea Waves ◽  
Mathematical Equations ◽  
Computational Hydraulics ◽  
Water Resources Engineering ◽  
Volume Method

The term hydraulics concerned with the conveyance of water that can consist of very simple processes to complex physical processes, such as flow in open rivers, flow in pipes, flow of nutrients/sediments, flow of ground water to sea waves. The study of hydraulics is primarily a mixture of theory and experiments. Computational hydraulics is very helpful in-order to quantify and predict flow nature and behavior. Mathematical model is backbone of the computational hydraulics that consist simple to complex mathematical equations with linear and/or non-linear terms and ordinary or partial differential equations. Analytical solution of this mathematical equations is not feasible in the majority of cases. In this consequences, mathematical models are solved using different numerical techniques and associated schemes. In this manuscript we will review hydraulic principles along with their mathematical equations. Then we will learn some commonly used numerical technique to solve different types of differential equations related to the hydraulics. Among them the Finite Difference Method (FDM), Finite Element Method (FEM) and Finite Volume Method (FVM) will be discussed along with their use in real-life applications in the context of water resources engineering.

scholarly journals Evolutionary algorithms, swarm intelligence methods, and their applications in water resources engineering: a state-of-the-art review

2020 ◽  
Vol 3 (1) ◽  
pp. 135-188 ◽  
Author(s):  
M. Janga Reddy ◽  
D. Nagesh Kumar
Keyword(s):  
Water Resources ◽  
Evolutionary Algorithms ◽  
Swarm Intelligence ◽  
Water Resource ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
State Of The Art ◽  
Real Life ◽  
Distribution Networks ◽  
Water Resources Engineering

Abstract During the last three decades, the water resources engineering field has received a tremendous increase in the development and use of meta-heuristic algorithms like evolutionary algorithms (EA) and swarm intelligence (SI) algorithms for solving various kinds of optimization problems. The efficient design and operation of water resource systems is a challenging task and requires solutions through optimization. Further, real-life water resource management problems may involve several complexities like nonconvex, nonlinear and discontinuous functions, discrete variables, a large number of equality and inequality constraints, and often associated with multi-modal solutions. The objective function is not known analytically, and the conventional methods may face difficulties in finding optimal solutions. The issues lead to the development of various types of heuristic and meta-heuristic algorithms, which proved to be flexible and potential tools for solving several complex water resources problems. This paper provides a review of state-of-the-art methods and their use in planning and management of hydrological and water resources systems. It includes a brief overview of EAs (genetic algorithms, differential evolution, evolutionary strategies, etc.) and SI algorithms (particle swarm optimization, ant colony optimization, etc.), and applications in the areas of water distribution networks, water supply, and wastewater systems, reservoir operation and irrigation systems, watershed management, parameter estimation of hydrological models, urban drainage and sewer networks, and groundwater systems monitoring network design and groundwater remediation. This paper also provides insights, challenges, and need for algorithmic improvements and opportunities for future applications in the water resources field, in the face of rising problem complexities and uncertainties.

scholarly journals Matrix computational collocation approach based on rational Chebyshev functions for nonlinear differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohamed A. Abd El Salam ◽  
Mohamed A. Ramadan ◽  
Mahmoud A. Nassar ◽  
Praveen Agarwal ◽  
Yu-Ming Chu
Keyword(s):  
Differential Equations ◽  
Numerical Technique ◽  
Nonlinear Differential Equations ◽  
Real Life ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Nonlinear Odes ◽  
Collocation Approach ◽  
Rational Chebyshev Functions ◽  
Rational Chebyshev

AbstractIn this work, a numerical technique for solving general nonlinear ordinary differential equations (ODEs) with variable coefficients and given conditions is introduced. The collocation method is used with rational Chebyshev (RC) functions as a matrix discretization to treat the nonlinear ODEs. Rational Chebyshev collocation (RCC) method is used to transform the problem to a system of nonlinear algebraic equations. The discussion of the order of convergence for RC functions is introduced. The proposed base is specified by its ability to deal with boundary conditions with independent variable that may tend to infinity with easy manner without divergence. The technique is tested and verified by two examples, then applied to four real life and applications models. Also, the comparison of our results with other methods is introduced to study the applicability and accuracy.

scholarly journals A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Khalid K. Ali ◽  
Mohamed A. Abd El salam ◽  
Emad M. H. Mohamed
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Fractional Order ◽  
Linear Functional ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Fractional Order Differential Equations ◽  
The Given ◽  
Functional Argument ◽  
Special Case

AbstractIn this paper, a numerical technique for a general form of nonlinear fractional-order differential equations with a linear functional argument using Chebyshev series is presented. The proposed equation with its linear functional argument represents a general form of delay and advanced nonlinear fractional-order differential equations. The spectral collocation method is extended to study this problem as a discretization scheme, where the fractional derivatives are defined in the Caputo sense. The collocation method transforms the given equation and conditions to algebraic nonlinear systems of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. A general form of the operational matrix to derivatives includes the fractional-order derivatives and the operational matrix of an ordinary derivative as a special case. To the best of our knowledge, there is no other work discussed this point. Numerical examples are given, and the obtained results show that the proposed method is very effective and convenient.

Use of Multiobjective Evolutionary Algorithms in Water Resources Engineering

2010 ◽  
pp. 45-82 ◽  
Author(s):  
Francisco Venícius Fernandes Barros ◽  
Eduardo Sávio Passos Rodrigues Martins ◽  
Luiz Sérgio Vasconcelos Nascimento ◽  
Dirceu Silveira Reis
Keyword(s):  
Water Resources ◽  
Evolutionary Algorithms ◽  
Multiobjective Evolutionary Algorithms ◽  
Water Resources Engineering

On obtaining limiting values of a class of infinite products

2018 ◽  
Vol 102 (555) ◽  
pp. 428-434
Author(s):  
Stephen Kaczkowski
Keyword(s):  
Difference Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Diffusion Theory ◽  
Numerical Technique ◽  
Applied Mathematics ◽  
Flow Analysis ◽  
Step Size ◽  
Infinite Products ◽  
Fluid Flow Analysis

Difference equations have a wide variety of applications, including fluid flow analysis, wave propagation, circuit theory, the study of traffic patterns, queueing analysis, diffusion theory, and many others. Besides these applications, studies into the analogy between ordinary differential equations (ODEs) and difference equations have been a favourite topic of mathematicians (e.g. see [1] and [2]). These applications and studies bring to light the similar character of the solutions of a difference equation with a fixed step size and a corresponding ODE.Also, an important numerical technique for solving both ordinary and partial differential equations (PDEs) is the method of finite differences [3], whereby a difference equation with a small step size is utilised to obtain a numerical solution of a differential equation. In this paper, elements of both of these ideas will be used to solve some intriguing problems in pure and applied mathematics.

Sign in / Sign up

Export Citation Format

Share Document