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1. Swim, Edward W. Nonconforming finite element methods for fluid-structure interaction problems.

Degree: Mathematics, 2005, Texas Tech University

URL: http://hdl.handle.net/2346/13652

Accurately simulating the interaction between a fluid and a structure remains a challenging problem in computational mathematics. One difficult aspect of this process is to efficiently couple the geometry of each domain as well as the systems of equations which model the physical properties of each media. The primary objective of this dissertation is to systematically develop and analyze Sophisticated computational techniques which employ finite element methods for solving fluid-structure interaction problems that arise in science and engineering applications.
First, a one-dimensional problem is presented in order to introduce the approximation techniques we will extend to higher dimensions. Additionally, many two-dimensional fluid-structure interactions can be reduced to one dimension under certain assumptions about the geometry of the subdomains along with inflow and outflow boundary conditions. In this context, we will establish consistency and stability properties for our discretization methods. Secondly, we will develop a nonconforming finite element methodology using a three-field formulation to solve a coupled physical system comprised of two adjacent domains, one containing a viscous, incompressible fluid and the other an elastic structure. Our method will employ an arbitrary Lagrangian-Eulerian strategy to formulate the governing equations for the fluid coupled with a linear elasticity model describing the deformation of the solid in order to simulate a full unsteady physical phenomenon. This formulation is analogous to the one used in the one-dimensional problem, although more complicated constraints are required due to the geometry of the problem. Again, consistency and stability properties are established for this technique. Finally, computational results which establish consistency and convergence of our numerical methods for the one-dimensional problem are presented.
These results include verification that our discretization technique is first order in time and that when a nonconforming technique is applied, i.e., when different polynomial degrees of approximation are used in the fluid and structure domains, the solution obtained is no worse than those computed using a conforming method. Additionally, convergence of the method under refinement of the computational grid, known as the h-method, is explored.
Thus, our numerical experiments provide confidence in the discretization techniques established in the previous chapters as well as insight on how to appropriately construct finite element code for the two-dimensional problem.
*Advisors/Committee Members: Seshaiyer, Padmanabhan (Committee Chair), Allen, Edward J. (committee member), Barnard, Roger W. (committee member), Manservisi, Sandro (committee member).*

Subjects/Keywords: Fluid-structure interaction; Nonconforming finite element methods; Finite elements

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Swim, E. W. (2005). Nonconforming finite element methods for fluid-structure interaction problems. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/13652

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Swim, Edward W. “Nonconforming finite element methods for fluid-structure interaction problems.” 2005. Thesis, Texas Tech University. Accessed October 27, 2020. http://hdl.handle.net/2346/13652.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Swim, Edward W. “Nonconforming finite element methods for fluid-structure interaction problems.” 2005. Web. 27 Oct 2020.

Vancouver:

Swim EW. Nonconforming finite element methods for fluid-structure interaction problems. [Internet] [Thesis]. Texas Tech University; 2005. [cited 2020 Oct 27]. Available from: http://hdl.handle.net/2346/13652.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Swim EW. Nonconforming finite element methods for fluid-structure interaction problems. [Thesis]. Texas Tech University; 2005. Available from: http://hdl.handle.net/2346/13652

Not specified: Masters Thesis or Doctoral Dissertation

Texas Tech University

2. Swim, Edward W. Nonconforming finite element methods for fluid-structure interaction.

Degree: Mathematics, 2005, Texas Tech University

URL: http://hdl.handle.net/2346/1351

Accurately simulating the interaction between a fluid and a structure remains a challenging problem in computational mathematics. One difficult aspect of this process is to efficiently couple the geometry of each domain as well as the systems of equations which model the physical properties of each media. The primary objective of this dissertation is to systematically develop and analyze sophisticated computational techniques which employ finite element methods for solving fluid-structure interaction problems that arise in science and engineering applications. First, a one dimensional problem is presented in order to introduce the approximation techniques we will extend to higher dimensions. Additionally, many two-dimensional fluid-structure interactions can be reduced to one dimension under certain assumptions about the geometry of the subdomains along with inflow and outflow boundary conditions. In this context, we will establish consistency and stability properties for our discretization methods. Secondly, we will develop a nonconforming finite element methodology using a three-field formulation to solve a coupled physical system comprised of two adjacent domains, one containing a viscous, incompressible fluid and the other an elastic structure. Our method will employ an arbitrary Lagrangian Eulerian strategy to formulate the governing equations for the fluid coupled with a linear elasticity model describing the deformation of the solid in order to simulate a full unsteady physical phenomenon. This formulation is analogous to the one used in the one-dimensional problem, although more complicated constraints are required due to the geometry of the problem. Again, consistency and stability properties are established for this technique. Finally, computational results which establish consistency and convergence of our numerical methods for the one dimensional problem are presented. These results include verification that our discretization technique is first order in time and that when a nonconforming technique is applied, i.e., when different polynomial degrees of approximation are used in the fluid and structure domains, the solution obtained is no worse than those computed using a conforming method. Additionally, convergence of the method under refinement of the computational grid, known as the h-method, is explored. Thus, our numerical experiments provide confidence in the discretization techniques established in the previous chapters as well as insight on how to appropriately construct finite element code for the two dimensional problem.
*Advisors/Committee Members: Seshaiyer, Padmanabhan (Committee Chair), Allen, Edward J. (committee member), Barnard, Roger W. (committee member), Manservisi, Sandro (committee member).*

Subjects/Keywords: Nonconforming; Finite elements; Fluid-structure interaction

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Swim, E. W. (2005). Nonconforming finite element methods for fluid-structure interaction. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/1351

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Swim, Edward W. “Nonconforming finite element methods for fluid-structure interaction.” 2005. Thesis, Texas Tech University. Accessed October 27, 2020. http://hdl.handle.net/2346/1351.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Swim, Edward W. “Nonconforming finite element methods for fluid-structure interaction.” 2005. Web. 27 Oct 2020.

Vancouver:

Swim EW. Nonconforming finite element methods for fluid-structure interaction. [Internet] [Thesis]. Texas Tech University; 2005. [cited 2020 Oct 27]. Available from: http://hdl.handle.net/2346/1351.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Swim EW. Nonconforming finite element methods for fluid-structure interaction. [Thesis]. Texas Tech University; 2005. Available from: http://hdl.handle.net/2346/1351

Not specified: Masters Thesis or Doctoral Dissertation

Texas Tech University

3. McGee, Wayne Michael. h-p-k least squares finite element methodology and implementation for fluid-structure interactions.

Degree: Mathematics, 2007, Texas Tech University

URL: http://hdl.handle.net/2346/15805

As the complexity of fully coupled physical modeling applications grows, both in the simultaneous representation of multiple types of physics as well as in the physical geometries of problem domains, the utility of directly specifiable, generally applicable, unconditionally consistent variational methodologies incorporated with conforming and nonconforming adaptive finite element discretizations becomes increasingly apparent. The intent of this dissertation is to describe the mathematical theory for a general problem-solving methodology, apply this theory to a particular one-dimensional fluid-structure interaction problem involving a moving mesh under an Arbitrary Lagrangian-Eulerian framework, representative of a particular two-dimensional problem of the same type in arterial blood flow analysis, and develop a C++ finite element component library for rapid modeling application development. We will present the complete fluid-structure application and some numerical error results verifying convergence of the method under h and p refinements for varying k values, where k is the order of global continuity of the finite element approximations.
*Advisors/Committee Members: Seshaiyer, Padmanabhan (Committee Chair), Allen, Edward J. (committee member), Ibragimov, Akif (committee member), Manservisi, Sandro (committee member), Aulisa, Eugenio (committee member).*

Subjects/Keywords: Fluid structure interaction; Finite element method

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

McGee, W. M. (2007). h-p-k least squares finite element methodology and implementation for fluid-structure interactions. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/15805

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

McGee, Wayne Michael. “h-p-k least squares finite element methodology and implementation for fluid-structure interactions.” 2007. Thesis, Texas Tech University. Accessed October 27, 2020. http://hdl.handle.net/2346/15805.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

McGee, Wayne Michael. “h-p-k least squares finite element methodology and implementation for fluid-structure interactions.” 2007. Web. 27 Oct 2020.

Vancouver:

McGee WM. h-p-k least squares finite element methodology and implementation for fluid-structure interactions. [Internet] [Thesis]. Texas Tech University; 2007. [cited 2020 Oct 27]. Available from: http://hdl.handle.net/2346/15805.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

McGee WM. h-p-k least squares finite element methodology and implementation for fluid-structure interactions. [Thesis]. Texas Tech University; 2007. Available from: http://hdl.handle.net/2346/15805

Not specified: Masters Thesis or Doctoral Dissertation