Past Event: Oden Institute Seminar

Four "better'' ways to solve the Navier-Stokes equations

Max Gunzburger, Professor, Mathematics, Florida State University

Abstract

Four "better'' ways to solve the Navier-Stokes equations: Ensemble discretization methods, an auxiliary equation approach for UQ, simulation of Richardson pair dispersion This facetious and self-serving title refers to four novel 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 is the case for uncertainty quantification, reduced-order modeling, control and optimization, and other applications. 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 the Navier-Stokes equations with hyperviscosity regularization and a regularization due to Ladyzhenskaya for which well posedness is proved for the PDE and its discretizations. The first topic will be talked about but because the three other topics cannot be covered in the time allotted, the talk will be preceded by a polling of the audience to select which topics will be talked about. [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.] Bio Max D. Gunzburger, Francis Eppes Distinguished Professor of Mathematics at Florida State University, is an American mathematician and computational scientist affiliated with the Florida State interdisciplinary Department of Scientific Computing. He was the 2008 winner of the SIAM W.T. and Idalia Reid Prize in Mathematics. His seminal research contributions include flow control, finite element analysis, superconductivity and Voronoi tessellations. He has also made contributions in the areas of aerodynamics, materials, acoustics, climate change, groundwater, image processing and risk assessment.