Related papers: New approach to deriving gas dynamics equations
The relation between Latttice Boltzmann Method, which has recently become popular, and the Kinetic Schemes, which are routinely used in Computational Fluid Dynamics, is explored. A new discrete velocity model for the numerical solution of…
By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
The drag force experienced by astronomical objects moving through gaseous media (gas dynamical friction) plays a crucial role in their orbital evolution. Ostriker (1999) derived a formula for gas dynamical friction by linear analysis, and…
Any gravitating mass traversing a relatively sparse gas experiences a retarding force created by its disturbance of the surrounding medium. In a previous contribution (Lee & Stahler 2011), we determined this dynamical friction force when…
For a class of evolution equations that possibly have only local solutions, we introduce a stochastic component that ensures that the solutions of the corresponding stochastically perturbed equations are global. The class of partial…
We introduce an application of the Quasi-Gasdynamic method for a solution of ideal magnetohydrodynamic equations in the modeling of compressible conductive gas flows. A time-averaging procedure is applied for all physical parameters in…
Shockwaves provide a useful and rewarding route to the nonequilibrium properties of simple fluids far from equilibrium. For simplicity, we study a strong shockwave in a dense two-dimensional fluid. Here, our study of nonlinear transport…
In the current work we propose a theory for an additional mass diffusion effect in the conventional gas dynamics equations. We find that this effect appears as a homogenization time limit correction, when the deterministic interaction…
We study the force of dynamical friction acting on a gravitating point mass that travels through an extended, isothermal gas. This force is well established in the hypersonic limit, but remains less understood in the subsonic regime. Using…
We propose a geometrical approach to the mechanics of continuous media equipped with inner structures and give the basic (mass conservation, Navier-Stokes and energy conservation) equations of their motion.
Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized…
The Navier-Stokes Hamiltonian is derived from first principles. Its Hamilton equations are shown to be equivalent to the continuity, Navier-Stokes, and energy conservation equations of a compressible viscous fluid. The derivations of the…
The viscosity and self-diffusion constant of particle-based mesoscale hydrodynamic methods, multi-particle collision dynamics (MPC) and dissipative particle dynamics (DPD), are investigated, both with and without angular-momentum…
A new formulation of the Navier-Stokes equation, in terms of the gradient of the total mechanical energy, is derived for the time-averaged flows, and the singular point possibly existing in the Navier-Stokes equation is exactly found.…
We present a mesoscopic hydrodynamic description of the dynamics of colloidal suspensions. We consider the system as a gas of Brownian particles suspended in a Newtonian heat bath subjected to stationary non-equilibrium conditions imposed…
We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier-Stokes equations for the volume averaged…
Starting from the fluctuating Boltzmann equation for smooth inelastic hard spheres or disks, closed equations for the fluctuating hydrodynamic fields to Navier-Stokes order are derived. This requires to derive constitutive relations for…