Mathematical Constraints in Multiscale Subgrid-Scale Modeling of Nonlinear Systems

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.