In fluid mechanics, the Navier-Stokes equations are non-linear partial differential equations that describe the motion of Newtonian fluids. A fluid can be a liquid or a gas. Therefore, the Navier-Stokes equation concerns many phenomena that surround us. The analytical resolution, the search for exact solutions of these equations modeling a fluid is difficult. But they often allow, by an approximate resolution, to propose a model of many phenomena, such as ocean currents and air mass movements in the atmosphere for meteorologists, the behavior of skyscrapers or bridges under the action of wind for architects and engineers, or that of airplanes, trains or high-speed cars for their design offices, as well as the flow of water in a pipe and many other flow phenomena of various fluids. In mathematics, nonlinearity complicates things. In physics, too, the difficulty arises. For this term nonlinearity has its translation in the complexity of the physical phenomena described. This difficulty of resolution partly affects the analyses or descriptions of the modeled phenomena. The objective of this work is the search for exact solutions of the Navier-Stokes equations in dimension 2 and in dimension 3. The method of the reduced differential transform is used to find the exact solutions of these Navier-Stokes equations in 2D and 3D. This method gives an algorithm that favors the rapid convergence of the problem to the exact solution sought. Besides the introduction, this article is structured as follows: the presentation of the method, its application on the two selected Navier-Stokes problems whose exact solutions are obtained with ease, then intervenes the conclusion of the whole work.
| Published in | Pure and Applied Mathematics Journal (Volume 11, Issue 6) |
| DOI | 10.11648/j.pamj.20221106.11 |
| Page(s) | 96-101 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Navier-Stokes Equation 2D, Navier-Stokes Equation 3D, Exact Solution, Reduced Differential Transform Method
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APA Style
Yanick Alain Servais Wellot. (2022). Application of the Reduced Differential Transform Method to Solve the Navier-Stokes Equations. Pure and Applied Mathematics Journal, 11(6), 96-101. https://doi.org/10.11648/j.pamj.20221106.11
ACS Style
Yanick Alain Servais Wellot. Application of the Reduced Differential Transform Method to Solve the Navier-Stokes Equations. Pure Appl. Math. J. 2022, 11(6), 96-101. doi: 10.11648/j.pamj.20221106.11
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Download@article{10.11648/j.pamj.20221106.11,
author = {Yanick Alain Servais Wellot},
title = {Application of the Reduced Differential Transform Method to Solve the Navier-Stokes Equations},
journal = {Pure and Applied Mathematics Journal},
volume = {11},
number = {6},
pages = {96-101},
doi = {10.11648/j.pamj.20221106.11},
url = {https://doi.org/10.11648/j.pamj.20221106.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221106.11},
abstract = {In fluid mechanics, the Navier-Stokes equations are non-linear partial differential equations that describe the motion of Newtonian fluids. A fluid can be a liquid or a gas. Therefore, the Navier-Stokes equation concerns many phenomena that surround us. The analytical resolution, the search for exact solutions of these equations modeling a fluid is difficult. But they often allow, by an approximate resolution, to propose a model of many phenomena, such as ocean currents and air mass movements in the atmosphere for meteorologists, the behavior of skyscrapers or bridges under the action of wind for architects and engineers, or that of airplanes, trains or high-speed cars for their design offices, as well as the flow of water in a pipe and many other flow phenomena of various fluids. In mathematics, nonlinearity complicates things. In physics, too, the difficulty arises. For this term nonlinearity has its translation in the complexity of the physical phenomena described. This difficulty of resolution partly affects the analyses or descriptions of the modeled phenomena. The objective of this work is the search for exact solutions of the Navier-Stokes equations in dimension 2 and in dimension 3. The method of the reduced differential transform is used to find the exact solutions of these Navier-Stokes equations in 2D and 3D. This method gives an algorithm that favors the rapid convergence of the problem to the exact solution sought. Besides the introduction, this article is structured as follows: the presentation of the method, its application on the two selected Navier-Stokes problems whose exact solutions are obtained with ease, then intervenes the conclusion of the whole work.},
year = {2022}
}
TY - JOUR T1 - Application of the Reduced Differential Transform Method to Solve the Navier-Stokes Equations AU - Yanick Alain Servais Wellot Y1 - 2022/11/22 PY - 2022 N1 - https://doi.org/10.11648/j.pamj.20221106.11 DO - 10.11648/j.pamj.20221106.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 96 EP - 101 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20221106.11 AB - In fluid mechanics, the Navier-Stokes equations are non-linear partial differential equations that describe the motion of Newtonian fluids. A fluid can be a liquid or a gas. Therefore, the Navier-Stokes equation concerns many phenomena that surround us. The analytical resolution, the search for exact solutions of these equations modeling a fluid is difficult. But they often allow, by an approximate resolution, to propose a model of many phenomena, such as ocean currents and air mass movements in the atmosphere for meteorologists, the behavior of skyscrapers or bridges under the action of wind for architects and engineers, or that of airplanes, trains or high-speed cars for their design offices, as well as the flow of water in a pipe and many other flow phenomena of various fluids. In mathematics, nonlinearity complicates things. In physics, too, the difficulty arises. For this term nonlinearity has its translation in the complexity of the physical phenomena described. This difficulty of resolution partly affects the analyses or descriptions of the modeled phenomena. The objective of this work is the search for exact solutions of the Navier-Stokes equations in dimension 2 and in dimension 3. The method of the reduced differential transform is used to find the exact solutions of these Navier-Stokes equations in 2D and 3D. This method gives an algorithm that favors the rapid convergence of the problem to the exact solution sought. Besides the introduction, this article is structured as follows: the presentation of the method, its application on the two selected Navier-Stokes problems whose exact solutions are obtained with ease, then intervenes the conclusion of the whole work. VL - 11 IS - 6 ER -
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