报告题目：

Direct Modeling for Computational Fluid Dynamics and

Unified Gas-kinetic Scheme for Non-equilibrium Flow Simulations

演讲人：

Prof. Kun Xu (徐昆)

（Hong Kong University of Science and Technology）

时间：2013年7月12日（周五）上午10:00-11:30

地点：力学所主楼312会议室

邀请人：孙泉华 研究员

报告摘要：

All partial differential equations for the description of flow motion have their intrinsic valid physical modeling scales, and these scales may not be compatible with the numerical mesh size. It will be difficult to directly discretize PDEs in a mesh size scale in the hope of developing reliable and consistent computational methods. In this talk, I will first introduce a new concept about direct modeling for the development of CFD methods, where the physical modeling will be done directly in a discretized space. The construction of the unified gas-kinetic scheme (UGKS) is an example under the above numerical principle.

With discretized particle velocity space, a UKGS for the entire Knudsen number flow has been constructed based on the model Boltzmann equation. In comparison with other existing kinetic schemes for the Boltzmann equation, the current method has no difficulty to get accurate Navier-Stokes solutions in the continuum flow regime with the time step being much larger than the particle collision time, and to capture rarefied flow phenomena, even the free molecular flow. The unified scheme is an extension of the gas-kinetic scheme (GKS) for the Navier-Stokes solutions to the rarefied flow regime with the discretization of particle velocity space. The success of the method is due to the coupling of particle transport and collision in the evaluation of local time-dependent gas distribution function at a cell interface. Due to this coupling, the gas distribution function will evolve from the kinetic scale particle free transport to the hydrodynamic scale wave interaction. Under UGKS principle, the dynamics of whole spectrum of governing equations from the Boltzmann to the Navier-Stokes has been recovered, and the specific  solution used numerically depends on the ratio of numerical cell size to the local particle mean free path. Many numerical examples will be presented.