Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates

Abstract Through the Lie symmetry analysis method, the axisymmetric, incompressible, and inviscid fluid is studied. The governing equations that describe the flow are the Euler equations. Under intensive observation, these equations do not have a certain solution localized in all directions ( r , t...

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Autores principales:	R. Sadat, Praveen Agarwal, R. Saleh, Mohamed R. Ali
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Euler equations Axisymmetric flow Lie point symmetries Analytical solutions Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/619a72f8b5a9471f8567c9bfc045536f
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spelling	oai:doaj.org-article:619a72f8b5a9471f8567c9bfc045536f2021-11-07T12:13:31ZLie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates10.1186/s13662-021-03637-w1687-1847https://doaj.org/article/619a72f8b5a9471f8567c9bfc045536f2021-11-01T00:00:00Zhttps://doi.org/10.1186/s13662-021-03637-whttps://doaj.org/toc/1687-1847Abstract Through the Lie symmetry analysis method, the axisymmetric, incompressible, and inviscid fluid is studied. The governing equations that describe the flow are the Euler equations. Under intensive observation, these equations do not have a certain solution localized in all directions ( r , t , z ) $(r,t,z)$ due to the presence of the term 1 r $\frac{1}{r}$ , which leads to the singularity cases. The researchers avoid this problem by truncating this term or solving the equations in the Cartesian plane. However, the Euler equations have an infinite number of Lie infinitesimals; we utilize the commutative product between these Lie vectors. The specialization process procures a nonlinear system of ODEs. Manual calculations have been done to solve this system. The investigated Lie vectors have been used to generate new solutions for the Euler equations. Some solutions are selected and plotted as two-dimensional plots.R. SadatPraveen AgarwalR. SalehMohamed R. AliSpringerOpenarticleEuler equationsAxisymmetric flowLie point symmetriesAnalytical solutionsMathematicsQA1-939ENAdvances in Difference Equations, Vol 2021, Iss 1, Pp 1-16 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Euler equations Axisymmetric flow Lie point symmetries Analytical solutions Mathematics QA1-939
spellingShingle	Euler equations Axisymmetric flow Lie point symmetries Analytical solutions Mathematics QA1-939 R. Sadat Praveen Agarwal R. Saleh Mohamed R. Ali Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates
description	Abstract Through the Lie symmetry analysis method, the axisymmetric, incompressible, and inviscid fluid is studied. The governing equations that describe the flow are the Euler equations. Under intensive observation, these equations do not have a certain solution localized in all directions ( r , t , z ) $(r,t,z)$ due to the presence of the term 1 r $\frac{1}{r}$ , which leads to the singularity cases. The researchers avoid this problem by truncating this term or solving the equations in the Cartesian plane. However, the Euler equations have an infinite number of Lie infinitesimals; we utilize the commutative product between these Lie vectors. The specialization process procures a nonlinear system of ODEs. Manual calculations have been done to solve this system. The investigated Lie vectors have been used to generate new solutions for the Euler equations. Some solutions are selected and plotted as two-dimensional plots.
format	article
author	R. Sadat Praveen Agarwal R. Saleh Mohamed R. Ali
author_facet	R. Sadat Praveen Agarwal R. Saleh Mohamed R. Ali
author_sort	R. Sadat
title	Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates
title_short	Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates
title_full	Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates
title_fullStr	Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates
title_full_unstemmed	Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates
title_sort	lie symmetry analysis and invariant solutions of 3d euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/619a72f8b5a9471f8567c9bfc045536f
work_keys_str_mv	AT rsadat liesymmetryanalysisandinvariantsolutionsof3deulerequationsforaxisymmetricincompressibleandinviscidflowinthecylindricalcoordinates AT praveenagarwal liesymmetryanalysisandinvariantsolutionsof3deulerequationsforaxisymmetricincompressibleandinviscidflowinthecylindricalcoordinates AT rsaleh liesymmetryanalysisandinvariantsolutionsof3deulerequationsforaxisymmetricincompressibleandinviscidflowinthecylindricalcoordinates AT mohamedrali liesymmetryanalysisandinvariantsolutionsof3deulerequationsforaxisymmetricincompressibleandinviscidflowinthecylindricalcoordinates
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Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates

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