FRIDAY, February 11, 2005
Time: 3:00 - 4:00 PM
Constant 1042

Prof. Taku Ohwada
Department of Aeronautics and Astronautics
Kyoto University

The numerical simulations for rarefied gas flows at non-zero Knudsen numbers require tremendous computational effort. The non-zero Knudsen number flows are nonequilibrium in sense of Boltzmann. The deviation from the local Maxwellian equilibrium state is of the order of the Knudsen number Kn, and exerts an appreciable influence on the physical state of the system through inter-molecular collisions. Thus, to numerically solve the Boltzmann equation for non-zero Knudsen number flows, one must ensure theoretically that the numerical error is much smaller than the Knudsen number, i.e., it is of higher order in Knudsen number Kn.

For applications in space science or gaseous flows in nano or micro devices, one is compelled to deal with flows with a wide range of Knudsen number, and some times one needs to couple the solutions of computational fluid dynamics (CFD) in equilibrium regions (i.e., Kn=0) to the solutions of the Boltzmann equation in nearly equilibrium or even nonequilibrium regions. Recently there is a great interest in the particle-continuum hybrid methods which employ the direct simulation Monte Carlo (DSMC) technique as the Boltzmann solver. However, due to its stochastic nature, DSMC is subjected to significant statistical noise and thus makes coupling a difficult undertaking. In this talk, we shall discuss our proposal of deterministic hybrid methods as alternatives to DSMC-CFD hybrid methods. The main idea of our proposal is to solve the Boltzmann equation with the level of sophistication and accuracy adapted to the problem, and to solve hydrodynamics with kinetic schemes based on the Boltzmann equation, and to ensure coupling between the two parts is theoretically consistent and numerically efficient. We will demonstrate the validity and the simplicity of the proposed deterministic hybrid approaches by using the conventional implicit finite difference method for the BGK equation and the gas-kinetic Navier-Stokes solver in some examples.