Invariant properties of systems of equations of the mechanics of inhomogeneous fluids

The invariant properties of the fundamental system of equations of the mechanics of inhomogeneous fluids and its widely used approximations are analysed by the methods of continuous group theory. Simplifying assumptions significantly alter the invariant properties of the systems of equations. Both e...

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Bibliographic Details
Published inJournal of applied mathematics and mechanics Vol. 75; no. 4; pp. 390 - 397
Main Authors Baidulov, V.G., Chashechkin, Yu.D.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 2011
Elsevier
Subjects
Approximation
Computational fluid dynamics
Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fluid flow
Fluids
Frames
Fundamental areas of phenomenology (including applications)
Invariants
Mathematical analysis
Physics
Symmetry
Invariant
Fluid mechanics
Boussinesq model
Modelling
Symmetry groups
Group theory
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Summary:The invariant properties of the fundamental system of equations of the mechanics of inhomogeneous fluids and its widely used approximations are analysed by the methods of continuous group theory. Simplifying assumptions significantly alter the invariant properties of the systems of equations. Both extending and contracting the admissible symmetry group can occur and provide evidence of the violation of the conditions of equivalence between the original and derived systems. For example, the use of the incompressibility and Boussinesq approximations leads to extension of the concept of an inertial reference frame to all frames moving relative to one another with arbitrary linear acceleration.
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ISSN:0021-8928
0021-8928
DOI:10.1016/j.jappmathmech.2011.09.003