Calculating Sub-grid Stresses

Craig Johansen

The Smagorinsky subgrid model calculates the sub-grid stress based upon an eddy viscosity. The eddy viscosity is calculated from a length and velocity scale. The length scale is the grid size and the velocity scale is defined as the grid size*S where S is the resolved strain rate. My question is, IS THIS RESOLVED STRAIN RATE AN INSTANTANEOUS VALUE (IN TIME) OR IS IT AN AVERAGE VALUE IN TIME.

At first I thought it would be an instantaneous value and a new eddy viscosity was calculated at each new time step, but then I thought that this might produce instabilities in the algorithm and some damping function or averaging must be used. Hopefully I am clear in stating my question

Thanks

Craig Johansen