Diffusion Limit Of Moment Closure Systems

As an important approach to approximate kinetic equations,the moment method plays a major role in model reduction and scientific computing.In recent years,with the establishment of the hyperbolic regularization framework,this method has gained more and more attention.In general,the moment closure systems are first-order partial differential equations with stiff source terms（also called relaxation systems）.It is crucial to analyze the dissipativity-preserving and the compatibility of the moment systems with classical hydrodynamics equations,which is the research content of this thesis.This research mainly focus on two fundamental equations:Boltzmann equation and radiative transfer equation.The results can be stated as follows.1)We point out that a kind of discrete velocity model of the Boltzmann-BGK equa-tion satisfies Yong’s entropy dissipation condition,which means that it inherits the H–theorem of the Boltzmann equation.2)As the Knudsen number tends to zero,we prove that the solution of arbitrary order global hyperbolic moment closure system of the Boltzmann equation with four types of collision terms converges to the solution of the classical Navier–Stokes equation,and we derive reasonable viscosity and thermal conductivity coefficients.3)We verify that the radiation hydrodynamics moment system satisfies Yong’s struc-tural stability condition,where the moment closure of the radiation transfer equation adopts the regularizedmoment method.Based on this,we prove the nonrelativis-tic limit of the radiation hydrodynamics moment system by constructing the asymptotic solution of the equation with initial–layer correction.