LAGRANGIAN-DENSITY DERIVATION OF THE EQUATIONS OF SINGLE-FLUID AND TWO-FLUID FLOWS

A CLAUSSE

International Journal of Heat and Technology

International Information and Engineering Technology Association

Año: 2003 vol. 21 p. 13 - 20

0392-8764

Variational principles for problems in fluid dynamics are discussed in the context of the general problem of finding an equivalent derivation of a system of equations by means of an optimization procedure. Starting with the extended Hamilton principle of least action for fields, the Lagrange equation for fields is derived, which is equivalent to the Euler-Lagrange equations of particle mechanics. It is shown that the equation of motion of an inviscid fluid can be derived from the Lagrangian density. In addition, the flow equations of a fluid dispersed in a continuum are derived from the average Lagrangian density, leading to the classical two-fluid model of two-phase flow. A possible way to solve the ill-posedness problem of the two-fluid model, by means of the correct averaging of the kinetic energy density of the mixture, is presented.