The Boundary Convergence of the Steady Zero-temperature-driven Hard Spheres
نویسنده
چکیده
We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional velocity space is a trivial generalization. More specifically the linear problem arising when the second gas dominates as a flow with constant velocity (and hence zero temperature) is considered. The boundary condition adopted consists of prescribing the outgoing velocity distribution at the wall. It is discovered that the presence of the boundary under general assumptions on the outgoing distribution ensures the convergence of a series of path integrals and thus a convenient representation for the solution is obtained.
منابع مشابه
The Boundary Structure of Zero-temperature Driven Hard Spheres
We study the fundamental problem of two gas species whose molecules collide as hard spheres in the presence of a flat boundary and with dependence on only one space dimension. More specifically the steady linear problem considered is the one arising when the second gas dominates as a flow moving towards the boundary with constant microscopic velocity (and hence zero temperature). The boundary c...
متن کاملSteady State Self-Diffusion at Low Density
We prove that the motion of a test particle in a hard sphere fluid in thermal equilibrium converges, in the Boltzmann-Grad limit, to the stochastic process governed by the linear Boltzmann equation. The convergence is in the sense of weak convergence of the path measures. We use this result to study the steady state of a binary mixture of hard spheres of different colors (but equal masses and d...
متن کاملComparison of three different numerical schemes for 2D steady incompressible lid-driven cavity flow
In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equatio...
متن کاملCreep Stress Redistribution Analysis of Thick-Walled FGM Spheres
Time-dependent creep stress redistribution analysis of thick-walled FGM spheres subjected to an internal pressure and a uniform temperature field is investigated. The material creep and mechanical properties through the radial graded direction are assumed to obey the simple power-law variation throughout the thickness. Total strains are assumed to be the sum of elastic, thermal and creep strain...
متن کاملThermo-elastic Analysis of Functionally Graded Thick- Walled Cylinder with Novel Temperature – Dependent Material Properties using Perturbation Technique
In this work, thermo – elastic analysis for functionally graded thick – walled cylinder with temperature - dependent material properties at steady condition is carried out. The length of cylinder is infinite and loading is consist of internal hydrostatic pressure and temperature gradient. All of physical and mechanical properties expect the Poisson's ratio are considered as multiplied an expone...
متن کامل