Mathematical Constraints in Multiscale Subgrid-Scale Modeling of Nonlinear Systems
Le Fang1,2, Ming-Wei Ge3**
1Laboratory of Mathematics and Physics, Ecole Centrale de Pékin, Beihang University, Beijing 100191 2Co-Innovation Center for Advanced Aero-Engine, Beihang University, Beijing 100191 3School of Renewable Energy, North China Electric Power University, Beijing 102206
Abstract：To shed light on the subgrid-scale (SGS) modeling methodology of nonlinear systems such as the Navier–Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.
2017, Vol. 34 
