Computational Mathematics and Scientific Computing Seminar

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Four “better” ways to solve the Navier-Stokes equations: simulation of Richardson pair dispersion, ensemble discretization methods, an auxiliary equation approach for UQ, and filtered regularizations

Speaker: Max Gunzburger, Florida State

Location: Warren Weaver Hall 1302

Date: April 12, 2019, 10 a.m.

Synopsis:

The facetious and self-serving title refers to four approaches for Navier-Stokes simulations. The first involves the analysis, numerical analysis, and an efficient implementation strategy for a recently proposed fractional Laplacian closure model that accounts for Richardson pair dispersion observed in turbulent flows. The second is the exploitation of accurate and widely applicable ensemble methods in settings in which multiple inputs need to be processed, as may be the case for uncertainty quantification, reduced-order modeling, and control and optimization. The third addresses the lack of regularity of solutions and the resultant loss of accuracy of approximations in the case of white or weakly correlated additive noise forcing. The fourth involves filtered spectral viscosity and hierarchical finite element methods for regularized Navier-Stokes equations. [One or more of these efforts is joint with Trian Iliescu, Nan Jian, Eunjun Lee, Ju Ming, Yuki Saka, Michael Schneier, Catalin Trenchea, Zhu Wang, Fefei Xu, and Wenju Zhao.]