A Nonlinear, SubGridscale Model for Incompressible Viscous Flow Problems

Authors:
William J. Layton
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1996

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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.