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The Hamiltonian Field Theory of the Von Mises Wave Equation: Analytical and Computational Issues

Part of: Infinite-dimensional Hamiltonian systems Foundations, constitutive equations, rheology Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  16 March 2016

Christian Cherubini  and
Simonetta Filippi
Christian Cherubini*
Affiliation:
Unit of Nonlinear Physics and Mathematical Modeling, Campus Bio-Medico, University of Rome, I-00128, Rome, Italy International Center for Relativistic Astrophysics – I.C.R.A., Campus Bio-Medico, University of Rome, I-00128, Rome, Italy
Simonetta Filippi
Affiliation:
Unit of Nonlinear Physics and Mathematical Modeling, Campus Bio-Medico, University of Rome, I-00128, Rome, Italy International Center for Relativistic Astrophysics – I.C.R.A., Campus Bio-Medico, University of Rome, I-00128, Rome, Italy
*
*Corresponding author. Email addresses:, [email protected] (C. Cherubini), [email protected] (S. Filippi)
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Abstract

The Von Mises quasi-linear second order wave equation, which completely describes an irrotational, compressible and barotropic classical perfect fluid, can be derived from a nontrivial least action principle for the velocity scalar potential only, in contrast to existing analog formulations which are expressed in terms of coupled density and velocity fields. In this article, the classicalHamiltonian field theory specifically associated to such an equation is developed in the polytropic case and numerically verified in a simplified situation. The existence of such a mathematical structure suggests new theoretical schemes possibly useful for performing numerical integrations of fluid dynamical equations. Moreover it justifies possible new functional forms for Lagrangian densities and associated Hamiltonian functions in other theoretical classical physics contexts.

Keywords

47.40.-x02.30.Jr11.10.Ef04.90.+eClassical field theoriesfluid dynamicspartial differential equationsnumerical methods

MSC classification

Secondary: 76A02: Foundations of fluid mechanics 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 37K05: Hamiltonian structures, symmetries, variational principles, conservation laws
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 3 , March 2016 , pp. 758 - 769
Copyright
Copyright © Global-Science Press 2016 

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