Vincent J. Ervin ¹, William J. Layton ², Monika Neda ²

We study the numerical errors in finite elements discretizations of a time relaxation model of fluid motion:
u(t) + u center dot del u + del(p) - nu del u + chi u* = f and del center dot u = 0
In this model, introduced by Stolz, Adams, and Kleisser, u* is a generalized fluctuation and chi the time relaxation parameter. The goal of inclusion of the chi u* is to drive unresolved fluctuations to sero exponentially. We study convergence of discretization of model to the model's solution as h, Delta t -> 0. Next we complement this with an experimental study of the effect the time relaxation term (and a nonlinear extension of it) has on the large scales of a flow near a transitional point. We close by showing that the time relaxation term does not alter shock speeds in the inviscid, compressible case, giving analytical confirmation of a result of Stolz, Adams, and Kleiser.