A new form of governing equations of fluids arising from Hamilton's principle

Sergey L. Gavrilyuk , Henri Gouin (1, 2)

1 LMMT - Laboratoire de Modélisation Mécanique et Thermodynamique, EA 2596
2 IUSTI - Institut universitaire des systèmes thermiques industriels

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.

Mots clés: Hamilton's principle; Symmetric forms; Dispersion relations

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Mathématiques générales [math.GM]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Sergey L. Gavrilyuk, Henri Gouin. A new form of governing equations of fluids arising from Hamilton's principle. International Journal of Engineering Science, 1999, 37 (12), pp.1495-1520. ⟨10.1016/S0020-7225(98)00131-1⟩. ⟨hal-00204738⟩