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Two Level Finite Element Approximation of Navier-Stokes Equations with Nonlinear Subgridscale Artificial Viscosity
by
John P. Roop
North Carolina A & T State University
Coauthors: Traian Iliescu
In this talk, we will review the concept of two-level finite element approximation schemes for the Navier-Stokes equations. We will review the results of a recent article of ours 1, in which finite element convergence estimates and scaling estimates and numerical results were proven for a two-level approximation scheme for the Smagorinsky model. At its core a two-level approximation scheme allows for the same order of convergence at a fraction of the computational cost. We then introduce results from a new study which includes the possibility of varying the type of nonlinear subgridscale artificial viscosity model used and numerical results in three spatial dimensions. It is interesting to note that choosing the correct scaling coefficients leads to improved performance of the numerical algorithm in question.
1J. Borggaard, T. Iliescu, H.K. Lee, J.P. Roop and H. Son, "A two-level discretization method for the Smagorinsky model, " Multiscale Modeling
Date received: September 2, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caww-17.