Technical Thrust Area

Computational Fluid Dynamics and Fluid-Structure Interaction

Chair: John Evans, University of Colorado-Boulder 
Vice-Chair: Jinhui Yan, University of Illinois at Urbana-Champaign
Members-at-Large: Artem Korobenko, University of Calgary
Hugo Casquero, University of Michigan - Dearborn

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Seminar Series

June 17, 2022; 4-5pm CDT

Kenji Takizawa, Waseda University
TitleSpace–Time Isogeometric Analysis of Heart Valves
Abstract: With the Space–Time Isogeometric Analysis (ST-IGA), the Team for Advanced Flow Simulation and Modeling (TAFSM) has been bringing solution to a wide-range of real-world problems with formidable computational challenges. The flow analysis of the heart valve is one of them. In this presentation, the ST-IGA key technology is overviewed. (i) A general-purpose NURBS mesh generation method for IGA in fluid mechanics with complex geometries. (ii) ST Slip Interface method, which helps the mesh generation and its motion. (iii) Mesh relaxation and mesh moving based on fiber-reinforced hyperelasticity and optimized zero-stress state, which can improve the mesh orthogonality of the parametric directions. (iv) ST Topology Change (ST-TC), which is a core technology to handle the actual contact between the valve leaflets without giving up the high-resolution boundary layer representation. (v) Constrained-Flow-Profile (CFP) Traction, which stabilizes the inflow velocity when the flow is driven by the pressure difference. The presentation will include a discussion of the heart valve computation performed. This is a joint work with Tayfun Tezduyar, Rice University.

April 19, 2022

Guglielmo Scovazzi, Duke University
The Shifted Boundary Method for CFD
Embedded/immersed/unfitted boundary methods obviate the need for continual re-meshing in many applications involving rapid prototyping and design with complex geometries. Unfortunately, many finite element embedded boundary methods are also difficult to implement due to the need to perform complex cell cutting operations at boundaries, and the consequences that these operations may have on the overall conditioning of the ensuing algebraic problems. We present a new, stable, and simple embedded boundary method, named “Shifted Boundary Method” (SBM), which eliminates the need to perform cell cutting. Boundary conditions are imposed on a surrogate discrete boundary, lying on the interior of the true boundary interface. We then construct appropriate field extension operators by way of Taylor expansions, with the purpose of preserving accuracy when imposing the boundary conditions. We demonstrate the SBM on large-scale porous media flow problems; incompressible flow problems governed by the Navier-Stokes equations (also including moving free surfaces); and problems governed by hyperbolic conservation laws.

February 22, 2022

Arif Masud, University of Illinois at Urbana-Champaign
TitleVariational Multiscale Discontinuous-Galerkin (VMDG) Method for Coupled Fluid-Solid Systems: Theory and Applications
Abstract: This talk presents a new class of Variational Multiscale methods with enhanced stability and accuracy properties for multifield problems with dominant interfacial phenomena and embedded constraints [1]. A multiscale decomposition of the unknown fields into coarse- and fine-scales leads to two coupled systems [2] that describe physics at the global and the local levels, respectively. The fine-scale system facilitates various modelling options, and an approach for variationally deriving analytical expressions for the fine-scale models is presented [3,4] that also results in a posteriori error estimator for the coupled field problem. Interface coupling terms are derived by embedding Discontinuous Galerkin (DG) ideas in the Variational Multiscale (VMS) framework and locally resolving the fine-scale variational equations from the fluid and the solid subdomains along the common interface [5]. A monolithic FSI method is developed for coupling incompressible viscous fluids with finitely deforming elastic solids across matching as well as non-matching interfacial meshes. A unique attribute of the VMDG method is the systematic procedure for deriving analytical expression for the traction Lagrange multiplier at the fluid-solid interface. The structure of the interface stabilization tensor emerges naturally and is shown to be a function of the boundary operators that are associated with the domain interior operators from the fluid and the solid subdomains. The method is extended to the class of problems where interfaces can traverse through the computational grids, giving rise to the Immersed Methods.
Fluid-solid coupling issues also arise in chemo-mechanically driven material evolution in finitely deforming solids that are permeated with advecting reactive fluids. These problems appear in the field of additive manufacturing. A mixture theory model is employed wherein kinematics is represented via independent set of balance laws for each of the interacting constituents [6]. Coupled chemo-mechanical effects and evolving nonlinearities give rise to spatially localized phenomena, namely, boundary layers, shear bands, and steep gradients that appear at the traversing reaction fronts and result in large local deformations. The enhanced stability and accuracy of the multiscale methods for fluid-solid coupling on overlapping domains is highlighted. Several test cases are presented to show the generality of the proposed methods and their application to problems of contemporary interest in science and engineering.
1) S. Kang, J. Kwack, A. Masud, Variational Coupling of Non-Matching Discretizations Across Finitely Deforming Fluid-Structure Interfaces, IJNMF, 2022,
2) T.J.R. Hughes, G.R. Feijoo, L. Mazzei, J.B. Quincy, The variational multiscale method-a paradigm for computational mechanics, CMAME 166 (1998) 3-24.
3) A. Masud and R. Calderer, A variational multiscale method for incompressible turbulent flows: Bubble functions and fine scale fields. CMAME, 200, 2577-2593, 2011.
4) A. Masud and T. Truster, A Framework for Residual-Based Stabilization of Incompressible Finite Elasticity: Stabilized Formulations and F-bar Methods for Linear Triangles and Tetrahedra. CMAME, 267, 359-399, 2013.
5) T. Truster and A. Masud, Primal interface formulation for coupling multiple PDEs: A consistent derivation via the Variational Multiscale method. CMAME, 268, 194-224, 2014.
6) M. Anguiano, H. Gajendran, RB. Hall, KR. Rajagopal, A. Masud, Chemo-mechanical coupling and material evolution in finitely deforming solids with advancing fronts of reactive fluids, Acta Mechanica, 231(5), 1933-1961, 2020.

January 28, 2022

Lucy Zhang, Rensselaer Polytechnic Institute
TitleNumerical Coupling Workflow of Multiphysics Interactions Using Immersed Methods
Abstract: Multiphysics and multiscale problems exist in many aspects of nature and practical engineering applications. Multiphysics involve multiple physical behaviors to be coupled for an inter-related response. Multiscale problems are to couple physical models at different length or time scales to achieve more precise and accurate description of physical behaviors. To obtain stable, effective, and accurate coupled solutions is not trivial. Traditional methods that are available in commercial software often generate numerical instabilities. To simulate and analyze engineering applications involving multiphysics and multiscales require robust simulation strategy and computational tool. In this talk, I will present the non-boundary-fitted mesh technique used initially in the Immersed Finite Element Method (IFEM) for fluid-structure interactions. I will discuss the evolvement of the immersed finite element method over the years and demonstrate its robustness as a numerical framework and how it can easily couple the physics of any co-existing phases and scales with overlapping meshing or grids represented with different frame of references and written in different numerical codes. The immersed framework has been packaged into an open-source software, OpenIFEM, with cross-platform build, standard testing with modularity, and user documentations. Finally, I will demonstrate its capability by show casing several biomedical and defense applications involving fluid-structure interactions, acoustics-fluid-structure interactions, and solid-solid impacts. 

December 9, 2021

Michael Sprague, National Renewable Energy Laboratory
TitlePredictive Simulations of Wind Turbines on Next-Generation Supercomputers
Abstract: In this talk I will describe our team’s effort to create the open-source ExaWind modeling and simulation environment for high-fidelity predictive wind-turbine and wind-plant simulations. Predictive, physics-based high-fidelity computational models, validated with targeted experiments, provide the most efficacious path to understanding wind plant physics and reducing wind plant losses. The ExaWind software stack has three physics solvers: Nalu-Wind, AMR-Wind, and OpenFAST. Nalu-Wind is an unstructured-grid computational-fluid-dynamics (CFD) code that is used to resolve complex geometry and capture thin boundary layers around blades. Nalu-Wind models are embedded in, and two-way coupled to, an AMR-Wind model through overset meshes. AMR-Wind is a structured-grid CFD code with adaptive-mesh-refinement capabilities and is built on the AMReX libraries. OpenFAST is a whole-turbine simulation code, which includes nonlinear blade dynamics, tower dynamics, and control system dynamics. High-performance computing (HPC) is key to high-fidelity wind farm simulations, but HPC is changing rapidly with many supercomputers, like the coming U.S. exascale-class supercomputers, that are relying on graphical processing units (GPUs) for efficiency. I will discuss our results from the Summit supercomputer, which is the second fastest machine in the world, and I will show full turbine simulation results that capture spatial scales spanning eight orders of magnitude.

November 4, 2021

Marilyn Smith, Georgia Tech
TitleHigh-Fidelity Aeroelasticity Simulations for Rotating Systems
Abstract: With the advent of the U.S. military’s Future Vertical Lift program and the surge of civilian applications in unmanned aerial systems (UAS) and Urban/Advanced Air Mobility (U/AAM), the ability to accurately and efficiently analyze the aeromechanics of novel flight vehicle designs with rotating systems has once again become a major focus of research. Rotating systems such as helicopter rotors, tilt rotors and large wind turbines must be both designed and evaluated using aeroelastic predictions where the causal physics are inherently nonlinear. The vertical lift and wind energy communities have developed a range of predictive methods to address these rotating systems. This seminar will discuss current and future methods of aeroelastic predictions using high-fidelity aerodynamics, namely CFD/CSD prediction methods and CFD-based dual-solver hybrid aeroelastic methods. Validation and sensitivity analysis of aeroelastic simulations with temporal- and spatialvariations, such as rotating systems, will also be explored.

October 14, 2021

Tayfun Tezduyar, Rice University
TitleSpace–Time Computational Analysis: From Inception to New Generations
Abstract: Space–Time VMS (ST-VMS) method and its predecessor ST-SUPS have a good track record in computational analysis of complex FSI and moving boundaries and interfaces (MBI). Challenging problems with successful analysis range from spacecraft parachutes to flapping-wing aerodynamics of an actual locust, from ventriclevalve-aorta flow to tire-aerodynamics with actual tire geometry, road contact and tire deformation. When an FSI or MBI problem requires high-resolution representation of boundary layers, methods where the mesh moves to follow the fluid–solid interface meet that requirement. Moving-mesh methods have been practical in more classes of complex problems than commonly thought of. With a number of complementary methods, the ST methods can now do even more. This is an overview of how the ST methods started and how they evolved over the years. It is joint work with Kenji Takizawa, Waseda

September 9, 2021

Yuri Bazilevs, Brown University
Title: Advanced and Practical Fluid-Structure Interaction
In this talk I will present the recent breakthroughs in advanced fluid-structure interaction (FSI) modeling that enable the application of what is largely considered by some "academic" methods to accurate and effective simulation of mechanical and structural systems. The presentation will focus on describing the modeling approaches involved and showing several convincing examples/studies from wind energy to air-blast FSI.