scholarly journals Computer Oriented Numerical Scheme for Solving Engineering Problems

2022 ◽  
Vol 42 (2) ◽  
pp. 689-701
Author(s):  
Mudassir Shams ◽  
Naila Rafiq ◽  
Nasreen Kausar ◽  
Nazir Ahmad Mir ◽  
Ahmad Alalyani
Keyword(s):  
Numerical Scheme ◽  
Engineering Problems

Convergence Stability of Through-Flow Analyses via the Implementation of the Secant and Bisection Iteration Schemes

2009 ◽  
Author(s):  
Vassilios Pachidis ◽  
Ioannis Templalexis ◽  
Pericles Pilidis
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Linear Equations ◽  
Original Form ◽  
Through Flow ◽  
Engineering Problems ◽  
Non Linear ◽  
Newton Raphson ◽  
Non Linear Equations

One of the most frequently encountered problems in engineering is dealing with non-linear equations. For example, the solution of the full Radial Equilibrium Equation (REE) in Streamline Curvature (SLC) through-flow methods is a typical case of a scientific analysis associated with a complex mathematical problem that can not be handled analytically. Various schemes are used routinely in scientific studies for the numerical solution of mathematical problems. In simple cases, these methods can be applied in their original form with success. The Newton-Raphson for example is one such scheme, commonly employed in simple engineering problems that require an iterative solution. Frequently however, the analysis of more complex phenomena may fall beyond the range of applicability of ‘textbook’ numerical methods, and may demand the design of more dedicated algorithms for the mathematical solution of a specific problem. These algorithms can be empirical in nature, developed from scratch, or the combination of previously established techniques. In terms of robustness and efficiency, all these different schemes would have their own merits and shortcomings. The success or failure of the numerical scheme applied depends also on the limitations imposed by the physical characteristics of the computational platform used, as well as by the nature of the problem itself. The effects of these constraints need to be assessed and taken into account, so that they can be anticipated and controlled. This manuscript discusses the development, validation and deployment of a convergence algorithm for the fast, accurate and robust numerical solution of the non-linear equations of motion for two-dimensional flow fields. The algorithm is based on a hybrid scheme, combining the Secant and Bisection iteration methods. Although it was specifically developed to address the computational challenges presented by SLC-type of analyses, it can also be used in other engineering problems. The algorithm was developed to provide a mid-of-the-range option between the very efficient but notoriously unstable Newton-Raphson scheme and other more robust, but less efficient schemes, usually employing some sort of Dynamic Convergence Control (DCC). It was also developed to eliminate the large user intervention, usually required by standard numerical methods. This new numerical scheme was integrated into a compressor SLC software and was tested rigorously, particularly at compressor operating regimes traditionally exhibiting convergence difficulties (i.e. part-speed performance). The analysis showed that the algorithm could successfully reach a converged solution, equally robustly but much more efficiently compared to a hybrid Newton-Raphson scheme employing DCC. The performance of these two schemes, in terms of speed of execution, is presented here. Typical error histories and comparisons of simulated results against experimental are also presented in this manuscript for a particular case-study.

NUMERICAL SCHEME OF THE WAHA CODE

2008 ◽  
Vol 20 (3-4) ◽  
pp. 323-354 ◽  
Author(s):  
Iztok Tiselj ◽  
A. Horvat ◽  
J. Gale
Keyword(s):  
Numerical Scheme

THE ROLE OF FINITE ELEMENT METHOD IN CIVIL ENGINEERING

2018 ◽  
Vol 5 (02) ◽  
Author(s):  
Er. Hardik Dhull
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Analytical Method ◽  
Civil Engineering ◽  
The Finite Element Method ◽  
Engineering Problems ◽  
Building Components ◽  
Element Method

The finite element method is a numerical method that is used to find solution of mathematical and engineering problems. It basically deals with partial differential equations. It is very complex for civil engineers to study various structures by using analytical method,so they prefer finite element methods over the analytical methods. As it is an approximate solution, therefore several limitationsare associated in the applicationsin civil engineering due to misinterpretationof analyst. Hence, the main aim of the paper is to study the finite element method in details along with the benefits and limitations of using this method in analysis of building components like beams, frames, trusses, slabs etc.

PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS

2020 ◽  
Author(s):  
A. I. Lopato ◽  
◽  
A. G. Eremenko ◽  
Keyword(s):  
Chemical Kinetics ◽  
Numerical Scheme ◽  
Unstructured Grids ◽  
Numerical Study ◽  
Numerical Approach ◽  
Detonation Waves ◽  
Detailed Chemical Kinetics ◽  
Parallel Solver ◽  
Further Development ◽  
Detailed Chemical

Recently, we developed a numerical approach for the simulation of detonation waves on fully unstructured grids and applied it to the numerical study of the mechanisms of detonation initiation in multifocusing systems. Current work is devoted to further development of our numerical approach, namely, parallelization of the numerical scheme and introduction of more comprehensive detailed chemical kinetics scheme.

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 91
Author(s):  
N. Sene
Keyword(s):  
Caputo Derivative ◽  
Local Stability ◽  
Numerical Scheme ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Maximal Lyapunov Exponent ◽  
Electrical Circuits ◽  
Adaptive Controls ◽  
Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

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