Related papers: New Virial Equation of State for Hard-Disk Fluids
We have used an extended Scaled-Particle Theory that incorporates four-body correlations through the fourth-order virial coefficient to analyse the orientational properties of a fluid of hard right-angle triangles. This fluid has been…
Here we present new results obtained for the equation of state with induced surface and curvature tensions. The explicit formulas for the first five virial coefficients of system pressure and for the induced surface and curvature tension…
We obtain estimates of all components of the velocity of a 3D rigid body moving in a viscous incompressible fluid without any symmetry restriction on the shape of the rigid body or the container. The estimates are in terms of suitable norms…
The energy route to the equation of state of hard-sphere fluids is ill-defined since the internal energy is just that of an ideal gas and thus it is independent of density. It is shown that this ambiguity can be avoided by considering a…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
Compressible flow varies from ideal-gas behavior at high pressures where molecular interactions become important. Density is described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and…
We introduce a new concept of dissipative varifold solution to models of two phase compressible viscous fluids. In contrast with the existing approach based on the Young measure description, the new formulation is variational combining the…
The virial expansion characterizes the high-temperature approach to the quantum-classical crossover in any quantum many-body system. Here, we calculate the virial coefficients up to the fifth-order of Fermi gases in 1D, 2D, and 3D, with…
In this paper we give a new formulation of the compressible Navier-Stokes by introducing an suitable effective velocity $v=u+\n\va(\rho)$ provided that the viscosity coefficients verify the algebraic relation of \cite{BD}. We give in…
In this paper the issue of the determination of the fluid pressure in incompressible fluids is addressed, with particular reference to the search of algorithms which permit to advance in time the fluid pressure without actually solving…
A homogenization approach is proposed for the treatment of porous wall boundary conditions in the computation of compressible viscous flows. Like any other homogenization approach, it eliminates the need for pore-resolved fluid meshes and…
We formulate the flow of thick fluids as evolution variational and quasi-variational inequalities, with a variable threshold on the absolute value of the deformation rate tensor. In the variational case, we show the existence and uniqueness…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
A novel stochastic fluid model is proposed with non-ideal structure factor consistent with compressibility, and adjustable transport coefficients. This Stochastic Hard Sphere Dynamics (SHSD) algorithm is a modification of the Direct…
An alternative to the well-known complete form of the Mie-Gr\"uneisen equation of state (EOS) for water is suggested. A closed analytical description of the self-consistent EOS for an arbitrary medium based only on the first law of…
We study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible Navier-Stokes-Fourier system. Our main result is the existence of a weak solution to these…
It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid coincides with the equations of motion of a charged {\it compressible} fluid moving due to a self-consistent electromagnetic field. Transition to the Lagrangian…
The rate of energy dissipation in solutions of the body-forced 3-d incompressible Navier-Stokes equations is rigorously estimated with a focus on its dependence on the nature of the driving force. For square integrable body forces the high…
We consider the compressible Navier-Stokes system with variable entropy. The pressure is a nonlinear function of the density and the entropy/potential temperature which, unlike in the Navier-Stokes-Fourier system, satisfies only the…