Related papers: Continuum mechanics of media with inner structures
We derive the 1D isentropic Euler and Navier-Stokes equations describing the motion of a gas through a nozzle of variable cross section as the asymptotic limit of the 3D isentropic Navier-Stokes system in a cylinder, the diameter of which…
We present a coordinate system for a general impulsive gravitational pp - wave in vacuum in which the metric is explicitly continuous, synchronous and "transverse". Also, it is more appropriate for investigation of particle motions.
We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…
Thin, solid bodies with metric symmetries admit a restricted form of reparameterization invariance. Their dynamical equilibria include motions with both rigid and flowing aspects. On such configurations, a quantity is conserved along the…
In this work, we show how the rheology of granular suspensions can be related to the properties of the fluctuations of the velocity field inside the medium. In particular, effective Navier-Stokes equations in the different flow regimes are…
A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time…
We introduce a modified version of the two-dimensional Navier-Stokes equation, preserving energy and momentum of inertia, which is motivated by the occurrence of different dissipation time scales and related to the gradient flow structure…
We present a technique that allows to obtain certain results in the compressible fluid theory: in particular, it is a nonexistence result for the highly decreasing at infinity solutions to the Navier-Stokes equations, the construction of…
We consider the motion of a rigid body, governed by the Navier-Stokes equations in a bounded domain. Navier's condition is prescribed on the boundary of the body. We give the global in a time solvability result of weak solution. The result…
Similar to the treatment of dense gases, fluid-dynamic equations for the dynamics of congested vehicular traffic are derived from Enskog-like kinetic equations. These contain additional terms due to the anisotropic vehicle interactions. The…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…
In this paper, we consider a mass conservation, positivity and energy identical-relation preserving scheme for the Navier-Stokes equations with variable density. Utilizing the square transformation, we first ensure the positivity of the…
Using an interpolant form for the gradient of a function of position, we write an integral version of the conservation equations for a fluid. In the appropriate limit, these become the usual conservation laws of mass, momentum and energy.…
Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative…
Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of…
A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged…
In this paper we give a general geometrical framework for working with problems that can be described as a structure-preserving submersion defined on a suitable space with a geometrical structure. We give many examples of how to formulate…
In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network…
We show a case of steady flow in a granular gas that, for small shear rates, is accurately described by Navier-Stokes hydrodynamics, even for high inelasticity. The (low density) granular gas is composed of identical inelastic spheres and…
We consider the two-dimensional motion of the coupled system of a viscous incompressible fluid and a rigid disc moving with the fluid, in the whole plane. The fluid motion is described by the Navier-Stokes equations and the motion of the…