Direct modeling-based computational fluid dynamics

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.