FRIDAY, February 11, 2005
Time: 11:00 - 12:00 PM
Gornto 222

Prof. Taku Ohwada
Department of Aeronautics and Astronautics
Kyoto University

High-resolution CFD schemes based on the kinetic theory of gases provide an alternative approach to the Riemann solver for capturing shock waves and contact discontinuities. The fact that the kinetic equation is linear in its convective term drastically simplifies the theory of characteristics. However, the asymptotic analysis that relates the kinetic equation to gas-dynamic or hydrodynamic equations is not familiar to the engineering community at large, thus it becomes an obstacle to understand the kinetic schemes. Also, this makes the error estimate of the kinetic approach difficult.

In this talk we will present a simple derivation of high-resolution kinetic schemes for the compressible Navier-Stokes equations, which does not require any advanced knowledge of kinetic theory, such as the Chapman-Enskog asymptotic expansion. We theoretically demonstrate that kinetic schemes can be simply constructed by considering certain basic properties of the equilibrium function and some well-known CFD techniques, such as the van Leer limiter. Several numerical tests are used to validate the proposed kinetic schemes.