Hamilton's principle of stationary action in multiphase flow modeling

Cosmin Burtea (1) , Sergey Gavrilyuk (2) , Charlotte Perrin (3)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 IUSTI - Institut universitaire des systèmes thermiques industriels
3 I2M - Institut de Mathématiques de Marseille

These lecture notes are concerned with the derivation of the fluid mechanics equations via Hamilton's principle of stationary action. We recall the main conceptual tools of this variational principle which originally applies to classical finite-degrees-of-freedom mechanics and we explain how these tools can be adapted in a continuous framework, in particular for the derivation of the well-known Euler equations describing the motion of inviscid fluids. The core of these notes is the application of Hamilton's principle to multiphase flows. We present a new Lagrangian point of view for the derivation of two-phase flow equations.

Domaines: Equations aux dérivées partielles [math.AP]

Cosmin Burtea, Sergey Gavrilyuk, Charlotte Perrin. Hamilton's principle of stationary action in multiphase flow modeling. 2021. ⟨hal-03146159⟩