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Unsteady Solutions of Euler Equations Generated bySteady Solutions

Unsteady Solutions of Euler Equations Generated bySteady Solutions Invariant solutions of partial differential equations are found by solving a reduced system involving one independent variable less. When the solutions are invariant with respect to the so-called projective group, the reduced system is simply the steady version of the original system. This feature enables us to generate unsteady solutions when steady solutions are known. The knowledge of an optimal system of subalgebras of the principal Lie algebra admitted by a system of differential equations provides a method of classifying H-invariant solutions as well as constructing systematically some transformations (essentially different transformations) mapping the given system to a suitable form. Here the transformations allowing to reduce the steady two-dimensional Euler equations of gas dynamics to an equivalent autonomous form are classified by means of the program SymboLie, after that an optimal system of two-dimensional subalgebras of the principal Lie algebra has been calculated. Some steady solutions of two-dimensional Euler equations are determined, and used to build unsteady solutions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Unsteady Solutions of Euler Equations Generated bySteady Solutions

Margheriti, L.; Speciale, M.
Acta Applicandae Mathematicae , Volume 113 (3) – Jan 4, 2011
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References (30)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer Science+Business Media B.V.
Subject
Mathematics; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics; Computer Science, general; Mathematics, general
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-010-9600-8
Publisher site
See Article on Publisher Site

Abstract

Invariant solutions of partial differential equations are found by solving a reduced system involving one independent variable less. When the solutions are invariant with respect to the so-called projective group, the reduced system is simply the steady version of the original system. This feature enables us to generate unsteady solutions when steady solutions are known. The knowledge of an optimal system of subalgebras of the principal Lie algebra admitted by a system of differential equations provides a method of classifying H-invariant solutions as well as constructing systematically some transformations (essentially different transformations) mapping the given system to a suitable form. Here the transformations allowing to reduce the steady two-dimensional Euler equations of gas dynamics to an equivalent autonomous form are classified by means of the program SymboLie, after that an optimal system of two-dimensional subalgebras of the principal Lie algebra has been calculated. Some steady solutions of two-dimensional Euler equations are determined, and used to build unsteady solutions.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Jan 4, 2011

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