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

Hamilton's Principle and Rankine-Hugoniot Conditions for General Motions of Mixtures

In previous papers, we have presented hyperbolic governing equations and jump conditions for barotropic fluid mixtures. Now we extend our results to the most general case of two-fluid conservative mixtures taking into account the entropies of components. We obtain governing equations for each component of the medium. This is not a system of conservation laws. Nevertheless, using Hamilton's principle we are able to obtain a complete set of Rankine-Hugoniot conditions. In particular, for the gas dynamics they coincide with classical jump conditions of conservation of momentum and energy. For the…

Continuum Mechanics and Thermodynamics in the Hamilton and the Godunov-type Formulations

Continuum mechanics with dislocations, with the Cattaneo type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov type system of the first order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time i…

Hyperbolic Models of Homogeneous Two-Fluid Mixtures

One derives the governing equations and the Rankine - Hugoniot conditions for a mixture of two miscible fluids using an extended form of Hamilton's principle of least action. The Lagrangian is constructed as the difference between the kinetic energy and a potential depending on the relative velocity of components. To obtain the governing equations and the jump conditions one uses two reference frames related with the Lagrangian coordinates of each component. Under some hypotheses on flow properties one proves the hyperbolicity of the governing system for small relative velocity of phases.

基于哈密顿原理导出的欧拉双曲传热模型：解析与数值研究

An Eulerian hyperbolic model for heat transfer derived via Hamilton's principle: analytical and numerical study

本文基于哈密顿原理在欧拉坐标下导出一个可压缩流传热新模型，证明其双曲性及与欧拉方程的渐近一致性，并通过解析与数值研究揭示其波动结构特性。

Hamiltonian variational formulation of three-dimensional, rotational free-surface flows, with a moving seabed, in the Eulerian description

Hamiltonian variational principles provided, since 60s, the means of developing very successful wave theories for nonlinear free-surface flows, under the assumption of irrotationality. This success, in conjunction with the recognition that almost all flows in the sea are not irrotational, raises the question of extending Hamilton Principle to rotational free-surface flows. The equations governing the fluid motion within the fluid domain, in the Eulerian description, have been derived by means of Hamilton Principle since late 50s. Nevertheless, a complete variational formulation of the problem,…

Rankine--Hugoniot conditions for fluids whose energy depends on space and time derivatives of density

By using the Hamilton principle of stationary action, we derive the governing equations and Rankine-Hugoniot conditions for continuous media where the specific energy depends on the space and time density derivatives. The governing system of equations is a time reversible dispersive system of conservation laws for the mass, momentum and energy. We obtain additional relations to the Rankine-Hugoniot conditions coming from the conservation laws and discuss the well-founded of shock wave discontinuities for dispersive systems.