A Nonlinear, Subgridscale Model for Incompressible viscous Flow Problems

Abstract

We consider a nonlinear subgridscale model of the Navier–Stokes equations resulting in a Ladyzhenskaya-type system. The difference is that the power “p” and scaling coefficient $\mu (h) \doteq O(h^\sigma )$ do not arise from macroscopic fluid properties and can be picked to ensure both $L^\infty $-stability and yet be of the order of the basic discretization error in smooth regions. With a properly scaled p-Laplacian-type artificial viscosity one can construct a higher-order method which is just as stable as first-order upwind methods.