Variational multiscale method for fluid-structure interaction on non-matching meshes and turbulent flows around immersed objects

This dissertation presents a novel computational framework for modeling interfacial physics across non-matching fluid-structure discretizations. Interfacial stabilized form is derived via the Variational Multiscale (VMS) framework employing the Discontinuous Galerkin (DG) ideas. For the derivation, we assume a multiscale decomposition of the weighting functions and the solution fields at the interface, which yields the coarse- and fine-scale subproblems. The key idea is to derive the fine-scale models that represents the discontinuities, and then variationally embed the fine-scale fields into the coarse-scale formulation. The fine-scale fields are modeled using edge basis functions, which enables the fine-scale problem to be locally solved on elements. The resulting interfacial terms weakly enforce the continuity conditions for coupling incompressible fluids and finitely deforming hyperelastic solids. The developed formulation is variationally consistent and free of user-defined parameters. A significant contribution is the form of stabilization tensors that are automatically calculated during simulations. This interfacial modeling method is generalized for the case of immersed objects in the fluid domain. The interfacial form weakly imposes the Dirichlet boundary conditions at the immersed boundaries that are independently defined from the background meshes. The stabilization tensor accounts for the material parameters, partial differential operators of the flow equations, time parameters, and the geometrical aspects of the cut elements. The method is sequentially extended for steady, unsteady, and turbulent flow problems. The residual-based turbulence model is employed for large-eddy simulation (LES). Because the method eliminates the necessity of nodally-matched or boundary-fitted discretization, it substantially reduces the time and effort to create meshes for numerical simulations around geometrically complex shapes, thereby bring CFD in each reach for a wider range of audiences. The mathematical attribute of the method is investigated using various numerical test cases ranging from standard benchmark problems to industrial and clinical applications. The convergence tests are carried out to confirm the optimal convergence of the formulation. Comparisons with the reference data on benchmark problems verify the accuracy of the numerical methods. The method is also tested for patient-specific cardiovascular models and industrial design applications to show its applicability to large-scale complex problems.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Kang, Soonpil

Contributors dc:contributor

• Masud, Arif
• Duarte, C. Armando
• Lopez-Pamies, Oscar
• Garcia, Marcelo H.

• computational fluid mechanics
• fluid-structure-interaction
• non-matching interface
• immersed boundary method
• turbulent flows

Statement dc:rights

• Copyright 2022 Soonpil Kang

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/115338

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115338