Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Ya Yan LU and Prof. Wei Wei SUN

Gas-kinetic Scheme for the Simulation from Free Molecule
to Navier-Stokes Solutions

by

Professor Kun Xu
Department of Mathematics
Hong Kong University of Science and Technology

Date: Apr 19, 2011 (Tuesday)
Time:4:30 pm to 5:30 pm
Venue: Room B6605 (College Conference Room)
Blue Zone, Level 6, Academic Building
City University of Hong Kong

ABSTRACT: With discretized particle velocity space, a unified gas-kinetic scheme for entire Knudsen number flows is constructed based on the kinetic models. In comparison with many existing kinetic schemes for the Boltzmann equation, the current method has no difficulty to get accurate solution in the continuum flow regime with the time step being much larger than the particle collision time, as well as the rarefied flow solution, even in the collisionless limit. The unified scheme is an extension of the gas-kinetic BGK-NS method for the continuum flow to the rarefied flow regime with the discretization of particle velocity space. The success of the method is due to the un-splitting treatment for the particle transport and collision in the evaluation of local time evolution of a gas distribution function, where both hydrodynamic and kinetic scale flow physics are included in the flux evaluation across a cell interface. The unified gas-kinetic scheme can simulate flows accurately in the whole flow. The unified scheme is a multiscale method with the update of both macroscopic flow variables and microscopic gas distribution function. In the continuum and transition flow regime, the unified scheme is much more efficient than the Direct Simulation Monte Carlo (DSMC) method. In this talk, we are going to introduce the methodology and numerical procedures in the construction of the unified scheme, and to present the reason: why we have to develop the kinetic scheme for the Boltzmann equation in this way.

** All interested are welcome **

For enquiry: 3442-9816