Variational Multiscale Immersed Boundary Method for Incompressible Turbulent Flows
This talk presents a new class of variational methods with enhanced stability properties for modeling incompressible flows. An immersed boundary method is developed that weakly enforces Dirichlet boundary conditions on immersed surfaces in stationary background discretizations. A stabilized interface form is derived by applying Variational Multiscale Discontinuous Galerkin (VMDG) ideas to the immersed boundaries, which may or may not coincide with the mesh nodal points. The weak form of the momentum balance equations is integrated with a residual-based turbulence model for incompressible turbulent flows. A significant contribution of this work is the variationally derived analytical expression for the Lagrange multiplier, which weakly enforces the velocity boundary conditions at the immersed surfaces. Additionally, the interfacial stabilization tensor accounts for the geometric aspects of the cut elements of the background mesh, and adapts both spatially and temporally as a function of the local flow physics at the embedded boundary. The method also provides a posteriori error estimator that can assess the local error in the weak enforcement of the essential boundary conditions. The method is demonstrated to work with meshes composed of hexahedral and tetrahedral elements. Test cases of increasing complexity are presented to validate the method on benchmark problems involving flows around cylindrical and spherical geometric shapes, with an analysis of the turbulent features of the flows.
Bio: Arif Masud is John and Eileen Blumenschein 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 also holds joint appointments as Professor of Biomedical and Translational Sciences in the Carle-Illinois College of Medicine. Dr. Masud has made fundamental and pioneering contributions to the development of Variational Multiscale (VMS) Methods for fluid and solid mechanics. He is President of the Engineering Mechanics Institute (EMI) of ASCE 2023-25, and has served as President of the Society of Engineering Science (SES) 2023. Dr. Masud has served as the Associate Editor (AE) of the ASCE Journal of Engineering Mechanics, and AE of the ASME Journal of Applied Mechanics. Dr. Masud was Chair of the Computational Mechanics Committee of ASCE, and Chair of the Fluid Mechanics Committee of ASME. He is an Associate Fellow of AIAA, and Fellow of USACM, IACM, AAM, ASME, EMI, and SES. Prof Masud was awarded the 2019 G.I. Taylor Medal by SES, and the 2022 Ted Belytschko Applied Mechanics Award by AMD-ASME for fundamental contributions to the Theory of Stabilized and Variational Multiscale Methods in Computational Mechanics.