Residual-based turbulence models for incompressible flows in domains with moving boundaries

Calderer Elias, Ramon

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https://hdl.handle.net/2142/31130 Copy

Description

Title

Residual-based turbulence models for incompressible flows in domains with moving boundaries

Author(s)

Calderer Elias, Ramon

Issue Date

2012-05-22T00:29:55Z

Director of Research (if dissertation) or Advisor (if thesis)

Masud, Arif

Doctoral Committee Chair(s)

Masud, Arif

Committee Member(s)

• Freund, Jonathan B.
• Heath, Michael T.
• Garcia, Marcelo H.
• Gropp, William D.

Department of Study

Civil & Environmental Eng

Discipline

Civil Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Turbulence modeling
• Moving boundaries
• Tetrahedral meshes
• Variational Multiscale method

Abstract

This dissertation presents residual-based turbulence models for problems with moving boundaries and interfaces. The method is derived employing the Variational Multiscale (VMS) framework, which gives rise to several modeling options that are exploited to obtain accurate turbulence models. To accommodate problems with moving boundaries such as fluid-structure interaction and free-surface problems, the formulation is cast in an Arbitrary Lagrangian-Eulerian (ALE) frame of reference. Multiple models of increasing degree of mathematical and algorithmic sophistication are presented. In all the cases, we assume a multiscale decomposition of the solution fields into overlapping components of different scale. The scales that can be accurately captured by the finite element discretization are numerically resolved, and are termed as the coarse scales, while the sub-grid scales, which may not be accurately represented by the finite element discretization, are termed as the fine-scales. The key idea of the VMS framework is to derive models for the fine scales in terms of the coarse scales, and then variationally project the fine-scale models onto coarse-scale space. This approach results in formulations that only depend on the coarse scales, while the effects of the fine scales on the coarse-scale fields are fully accounted for via the additional terms that arise due to the multiscale decomposition of the solution fields. In this dissertation, the fine scales are modeled using a bubble functions approach. This enables the fine-scale problem to be solved on elements or patches of elements. As a consequence, the presented algorithms are amenable for parallel implementation. The simplest fine-scale model presented here is derived introducing up-winding ideas to the discrete problem that governs the fine scales. To derive expressions for more sophisticated fine-scale models, VMS ideas are also applied to the fine-scale sub-problem. A significant feature of the bubble functions approach adopted here is that the derived turbulence models are free of any embedded or tunable parameters. Another significant feature of the method is that it is mathematically consistent because the fine-scale models are driven by the residual of the Euler-Lagrange equations for the coarse scales. Consequently, when the coarse scales are able to represent the exact solution of the problem, the fine-scale models vanish. Numerical attributes of the developed models are investigated via an exhaustive set of numerical tests. One of the classes of problems investigated has fix boundaries while the other has moving boundaries. The results are compared to reference experimental and numerical results, and excellent agreements are observed.

Graduation Semester

2012-05

Permalink

http://hdl.handle.net/2142/31130

Copyright and License Information

Copyright 2012 Ramon Calderer Elias

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