Heat Transfer in the Transition Regime: Solution of Boundary Value
Problems for Grad's Moment Equations via Kinetic Schemes
Abstract
The laws of Navier-Stokes and Fourier fail in the description of
rarefied gas flows, where the mean free path of the
gas molecules becomes substantially large. Typical examples are the
reentry of space craft into the earth's atmosphere and microscale flows
as well as electron transport in semiconductors and radiative transfer.
Processes in rarefied gases are well discribed by the Boltzmann
equation, but its solution - usually via Monte Carlo
methods - is very time expensive. Thus, efficient simulation of rarefied
gases requires improved
models which capture the main features of the flow at lower
computational cost.
In this talk we consider Grad's moment method for the description of
rarefied gases. In this method, the Boltzmann
equation is replaced by extended sets of moment equations, which can be
solved considerably fast. Which and how many moments are needed depends
on the particular process.
Boundary value problems for the moment equations are solved by a
numerical method, the so-called kinetic schemes. In this schemes, the
boundary conditions for the moments follow directly from the boundary
conditions for the Boltzmann equation.
This method allows for the first time a systematic approach to boundary
value for moment equations. For the case of
stationary heat transfer the results are convincing. In particular they
exhibit temperature jumps at the walls and boundary layers; the results
converge with increasing number of moments.
