A new form of governing equations of fluids arising from Hamiltons principleReport as inadecuate

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1 MSNMGP - Modélisation et Simulation Numérique en Mécanique et Génie des Procédés 2 LMMT - Laboratoire de Modélisation Mécanique et Thermodynamique, EA 2596

Abstract : A new form of governing equations is derived from Hamilton-s principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space.
This form yields conservation laws both for non-dispersive case Lagrangian depends only on conserved quantities and dispersive case Lagrangian depends also on their derivatives.
For non-dispersive case the set of conservation laws allows to rewrite the governing equations in the symmetric form of Godunov-Friedrichs-Lax.
The linear stability of equilibrium states for potential motions is also studied.
In particular, the dispersion relation is obtained in terms of Hermitian matrices both for non-dispersive and dispersive case.
Some new results are extended to the two-fluid non-dispersive case.

Keywords : Hamilton-s principle Symmetric forms Dispersion relations

Author: Sergey Gavrilyuk Henri Gouin -

Source: https://hal.archives-ouvertes.fr/


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