【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.更多还原

【Abstract】 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.更多还原