Volume 19, Issue 3
The Hamiltonian Field Theory of the Von Mises Wave Equation: Analytical and Computational Issues

Christian Cherubini & Simonetta Filippi

Commun. Comput. Phys., 19 (2016), pp. 758-769.

Published online: 2018-04

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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 classical Hamiltonian 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.

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@Article{CiCP-19-758, author = {}, title = {The Hamiltonian Field Theory of the Von Mises Wave Equation: Analytical and Computational Issues}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {3}, pages = {758--769}, 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 classical Hamiltonian 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.101114.140715a}, url = {http://global-sci.org/intro/article_detail/cicp/11108.html} }
TY - JOUR T1 - The Hamiltonian Field Theory of the Von Mises Wave Equation: Analytical and Computational Issues JO - Communications in Computational Physics VL - 3 SP - 758 EP - 769 PY - 2018 DA - 2018/04 SN - 19 DO - http://dor.org/10.4208/cicp.101114.140715a UR - https://global-sci.org/intro/article_detail/cicp/11108.html KW - AB -

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 classical Hamiltonian 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.

Christian Cherubini & Simonetta Filippi. (2020). The Hamiltonian Field Theory of the Von Mises Wave Equation: Analytical and Computational Issues. Communications in Computational Physics. 19 (3). 758-769. doi:10.4208/cicp.101114.140715a
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