Related papers: Variational formulation of a general dissipative f…
We present a mechanistic model for a Newtonian fluid called fluid particle dynamics. By analyzing the concept of ``fluid particle'' from the point of view of a Voronoi tessellation of a molecular fluid, we propose an heuristic derivation of…
The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…
Numerical models of weather and climate critically depend on long-term stability of integrators for systems of hyperbolic conservation laws. While such stability is often obtained from (physical or numerical) dissipation terms, physical…
A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by use of tensor-valued differential forms that allow to describe describe the…
We discuss heat conductivity from the point of view of a variational multi-fluid model, treating entropy as a dynamical entity. We demonstrate that a two-fluid model with a massive fluid component and a massless entropy can reproduce a…
In this paper, two approaches for modeling three-component fluid flows using diffusive interface method are discussed. Thermodynamic consistency of the proposed models is preserved when using an energetic variational framework to derive the…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
We develop a unified geometric framework for mechanical systems that combine conservative and dissipative dynamics by formulating them on contact manifolds. Within this setting, we identify the Reeb vector field as the intrinsic generator…
The first-order general relativistic theory of a generic dissipative (heat-conducting, viscous, particle-creating) fluid is rediscussed from a unified covariant frame-independent point of view. By generalizing some previous works in the…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic…
Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms…
From Hamilton's principle of stationary action, we derive governing equations of two-fluid mixtures and extend the model to the dissipative case without chemical reactions. For both conservative and dissipative cases, an algebraic identity…
The restriction of hydrodynamics to non-viscous, potential (gradient, irrotational) flows is a theory both simple and elegant; a favorite topic of introductory textbooks. It is known that this theory can be formulated as an action principle…
Single component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances, then the related thermodynamic relations and the entropy production are calculated…
The GENERIC structure allows for a unified treatment of different discrete models of hydrodynamics. We first propose a finite volume Lagrangian discretization of the continuum equations of hydrodynamics through the Voronoi tessellation. We…
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…
We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…
Hamilton's principle is extended to have compatible initial conditions to the strong form. To use a number of computational and theoretical benefits for dynamical systems, the mixed variational formulation is preferred in the systems other…
A new approach to dissipative quantum systems modelled by a system plus environment Hamiltonian is presented. Using a continuous sequence of infinitesimal unitary transformations the small quantum system is decoupled from its…