We propose and analyze a finite element method for approximating solutions to the Navier-Stokes-alpha model (NS-) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly improves accuracy in simulations. Standard finite element schemes for NS- suffer from two major sources of error if their solutions are considered approximations to true fluid flow: (1) the consistency error arising from filtering; and (2) the dramatic effect of the large pressure error on the velocity...

We consider an uncoupled, modular regularization algorithm for approximation of the Navier-Stokes equations. The method is: Step 1.1: Advance the NSE one time step, Step 1.1: Regularize to obtain the approximation at the new time level. Previous analysis of this approach has been for specific time stepping methods in Step 1.1 and simple stabilizations in Step 1.1. In this report we extend the mathematical support for uncoupled, modular stabilization to (i) the more complex and better performing...

We propose and analyze a finite element method for approximating solutions to the Navier-Stokes-alpha model (NS-) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly
improves accuracy in simulations. Standard finite element schemes
for NS- suffer from two major sources of error if their solutions are considered approximations
to true fluid flow: (1) the consistency error arising from filtering; and (2) the dramatic effect of the large pressure error
on the...

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