离散空间直接建模的计算流体力学方法  

Direct modeling-based computational fluid dynamics

作　　者：徐昆[1,4] 李启兵[2] 黎作武[3] 

机构地区：[1]香港科技大学数学系,中国香港 [2]清华大学航天航空学院,北京100084 [3]中国空气动力研究与发展中心,绵阳621000 [4]北京大学湍流和复杂系统国家重点实验室,北京100871

出　　处：《中国科学：物理学、力学、天文学》2014年第5期519-530,共12页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(批准号:11172154);香港大学教育资助委员会(编号:621011)资助项目

摘　　要：本文提出了一种发展适合多尺度、多物理流动的CFD格式的全新途径,即直接在离散空间利用物理模型的跨尺度演化解来建立数值格式的新方法.与直接离散偏微分方程的传统做法相比,基于离散空间直接建模构造出的数值方法考虑了网格尺度和物理模型之间的匹配,能做到不同尺度上物理模型的连续过渡,从而实现对多尺度流动的高效模拟.Boltzmann方程的模型演化解为直接建模方法提供了重要的支撑.本文提出了直接建模构造计算流体力学方法的理论基础,并给出了在建立统一气体动理学格式中的成功运用,验证了新方法的可行性和优越性.A new principle for constructing CFD scheme for multiscale and multiphysics flow computation is proposed. The principle is about the direct modeling in the discrete space and the use of cross-scale time evolution solution in the construction of numerical method. In comparison with traditional CFD method, where a direct discretization is used for the partial differential equation （PDE）, the new numerical methodology takes into account the mesh size effect and its associated evolution solution in the mesh size scale. As a result, with the variation of mesh size with respect to the local particle mean free path, a continuous spectrum of gas evolution model from the kinetic to the hydrodynamic scales can be recovered. For many multiscale flow problems, the governing equations may not be available, but the direct modeling can be still used to simulate different scale gas evolution process. The cross-scale time evolution solution from the model Boltzmann equation plays a central role in the direct modeling. Based on the direct modeling principle, the unified gas-kinetic scheme for the entire Knudsen number flow has been constructed. The excellent performance of the scheme validates the feasibility and advantage of the present CFD principle.

关 键 词：偏微分方程数值解 离散空间直接建模 多尺度流动 统一气体动理学格式 BGK方程 

分 类 号：O35[理学—流体力学]