Hierarchical Variational Frameworks for Multi-Field Problems in Solids and Fluids: A Unification of Concepts
Arif Masud
Professor, Department of Civil and Environmental Engineering
University of Illinois at Urbana-Champaign
This talk presents a new class of hierarchical variational methods with enhanced stability and accuracy properties for nonlinear multi-physics problems with dominant interfacial phenomena, embedded constraints, and weak and strong discontinuities. A multiscale decomposition of the unknown fields into coarse and fine scales leads to two coupled systems that describe physics at the global and local levels, respectively. Structure of the multiscale framework facilitates kernel functions for direct embedding of experimental/sensor data in the variational constructs to augment physics-based modeling with data driven modeling. The fine-scale system facilitates various modeling options that are systematically exploited to derive (i) techniques for consistent coupling of multiple interacting PDEs that govern physics on adjoining subdomains, (ii) develop quantum to quasi-continuum coupling techniques via residual based transfer of information, and (iii) derive residual-based closure models for turbulence. The framework is equipped with adjoint-based error estimation feature that emanates naturally in the development of the method. Several examples are presented to highlight the generality of the proposed methods and their application to problems of contemporary interest in science and engineering.
Arif Masud is Professor of Mechanics and Computations in the Department of Civil and Environmental Engineering, and the Department of Aerospace Engineering, at the University of Illinois at Urbana-Champaign. He has made fundamental and pioneering contributions to the development of Stabilized and Variational Multiscale Methods for fluid and solid mechanics, residual-based Turbulence models, non-Newtonian fluids, and Mixture Theory Models for chemically reacting porous media flows. He is past Chair of the Fluid Mechanics Committee of ASME, past Chair of the Computational Mechanics Committee of ASCE. Dr. Masud has served as an Associate Editor of the ASME Journal of Applied Mechanics, AE of the ASCE Journal of Engineering Mechanics, and currently serves as the AE of the International Journal of Multiscale Computational Engineering. He was the Co-Chair of the Finite Elements in Flow Problems Conference (FEF 2019) and is serving as the Co-Chair for the US National Congress on Computational Mechanics (USNCCM 2021). Dr. Masud is an Associate Fellow of AIAA, and Fellow of USACM, IACM, AAM, ASME, EMI (ASCE), and SES. He has been awarded the 2019 G.I. Taylor Medal by the Society of Engineering Science.
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