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1. Fuchs, Ashlee. An investigation of the effectiveness of block preconditioners on a non-Newtonian blood flow model.

Degree: Mathematics and Statistics, 2011, Texas Tech University

URL: http://hdl.handle.net/2346/ETD-TTU-2011-05-1476

Newtonian and non-Newtonian fluid flow can be modeled by the steady-state incompressible Navier-Stokes equations. Developing a non-Newtonian blood flow model is the particular problem of interest for this thesis. The process of solving this problem involves utilizing iterative solvers which can perform with higher accuracy and efficiency if properly preconditioned. Physics-based preconditioners have been developed for solving the steady-state incompressible Navier-Stokes equations. The primary aim of this thesis is to apply the pressure convection-diffusion (PCD) preconditioner to a non-Newtonian flow model in order to investigate effectiveness.
*Advisors/Committee Members: Howle, Victoria E. (Committee Chair), Kirby, Robert C. (committee member), Long, Kevin (committee member).*

Subjects/Keywords: Incompressible navier-stokes equations; Non-Newtonian; Pressure convection-diffusion preconditioner

Record Details Similar Records

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

APA (6^{th} Edition):

Fuchs, A. (2011). An investigation of the effectiveness of block preconditioners on a non-Newtonian blood flow model. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/ETD-TTU-2011-05-1476

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):

Fuchs, Ashlee. “An investigation of the effectiveness of block preconditioners on a non-Newtonian blood flow model.” 2011. Thesis, Texas Tech University. Accessed August 09, 2020. http://hdl.handle.net/2346/ETD-TTU-2011-05-1476.

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

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Fuchs, Ashlee. “An investigation of the effectiveness of block preconditioners on a non-Newtonian blood flow model.” 2011. Web. 09 Aug 2020.

Vancouver:

Fuchs A. An investigation of the effectiveness of block preconditioners on a non-Newtonian blood flow model. [Internet] [Thesis]. Texas Tech University; 2011. [cited 2020 Aug 09]. Available from: http://hdl.handle.net/2346/ETD-TTU-2011-05-1476.

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

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Fuchs A. An investigation of the effectiveness of block preconditioners on a non-Newtonian blood flow model. [Thesis]. Texas Tech University; 2011. Available from: http://hdl.handle.net/2346/ETD-TTU-2011-05-1476

Not specified: Masters Thesis or Doctoral Dissertation

2. Gohlke, Jedidiah W. A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations.

Degree: Mathematics and Statistics, 2011, Texas Tech University

URL: http://hdl.handle.net/2346/ETD-TTU-2011-08-1809

The incompressible Navier-Stokes equations model the relationship between the velocity and pressure of a ﬂuid and can be used to describe the motion of a ﬂuid. Because they are nonlinear, they are in most cases diﬃcult or impossible to solve
analytically. They must, therefore, be approximated numerically. One approach
developed by Alexandre Chorin is to use a projection method to approximate the pressure and velocity. We will look at Chorin’s approach and then consider a
modiﬁed approach called the gauge method, which mitigates some of the boundary condition diﬃculties in Chorin’s approach. We will then consider an improvement to the gauge method that gives us second order convergence in the velocity in both time and space and slightly better than order 3/2 convergence in the pressure in time. We will then present a code to automate the gauge method and consider some test cases to verify that the code converges at the appropriate rate.
*Advisors/Committee Members: Long, Kevin (Committee Chair), Howle, Victoria E. (committee member), Kirby, Robert C. (committee member), Hoang, Luan (committee member).*

Subjects/Keywords: Navier-Stokes equations; Projection method; Gauge method; Code validation

…*Texas* *Tech* *University*, Jedidiah Wayne Gohlke, August 2011
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Record Details Similar Records

❌

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

APA (6^{th} Edition):

Gohlke, J. W. (2011). A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/ETD-TTU-2011-08-1809

Not specified: Masters Thesis or Doctoral Dissertation

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

Gohlke, Jedidiah W. “A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations.” 2011. Thesis, Texas Tech University. Accessed August 09, 2020. http://hdl.handle.net/2346/ETD-TTU-2011-08-1809.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Gohlke, Jedidiah W. “A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations.” 2011. Web. 09 Aug 2020.

Vancouver:

Gohlke JW. A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations. [Internet] [Thesis]. Texas Tech University; 2011. [cited 2020 Aug 09]. Available from: http://hdl.handle.net/2346/ETD-TTU-2011-08-1809.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gohlke JW. A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations. [Thesis]. Texas Tech University; 2011. Available from: http://hdl.handle.net/2346/ETD-TTU-2011-08-1809

Not specified: Masters Thesis or Doctoral Dissertation

Texas Tech University

3. Cakmak, Adem. Analysis of nonlinear Darcy-Forchheimer flows in porous media.

Degree: Mathematics, 2009, Texas Tech University

URL: http://hdl.handle.net/2346/8729

This thesis is focused on certain theoretical aspects of nonlinear non-Darcy flows in porous media, and their application in reservoir and hydraulic engineering. The goal of this work is to develop a mathematically rigorous framework to study the dynamical processes associated to all three classical nonlinear Forchheimer laws for slightly compressible fluids. In our approach each anisotropic Forchheimer equation is replaced by a constitutive equation which relates the velocity vector field with the pressure gradient in a non-linear way. This allows reducing the original system of equations to one degenerate parabolic equation for the pressure only. It is shown that under some hydrodynamic and thermodynamic constraints there exists stable equilibrium: pseudo-steady state regime for the Forchheimer flows in porous media, which serves as a global attractor for wide classes of the flows yielding an alternative time independent computation of productivity index/diffusive capacity of a well.
*Advisors/Committee Members: Aulisa, Eugenio (Committee Chair), Ibragimov, Akif (Committee Chair), Kirby, Robert C. (committee member), Rengasamy, Raghunathan (committee member).*

Subjects/Keywords: Nonlinear Darcy-Forchheimer flow; Porous media

Record Details Similar Records

❌

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

APA (6^{th} Edition):

Cakmak, A. (2009). Analysis of nonlinear Darcy-Forchheimer flows in porous media. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/8729

Not specified: Masters Thesis or Doctoral Dissertation

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

Cakmak, Adem. “Analysis of nonlinear Darcy-Forchheimer flows in porous media.” 2009. Thesis, Texas Tech University. Accessed August 09, 2020. http://hdl.handle.net/2346/8729.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Cakmak, Adem. “Analysis of nonlinear Darcy-Forchheimer flows in porous media.” 2009. Web. 09 Aug 2020.

Vancouver:

Cakmak A. Analysis of nonlinear Darcy-Forchheimer flows in porous media. [Internet] [Thesis]. Texas Tech University; 2009. [cited 2020 Aug 09]. Available from: http://hdl.handle.net/2346/8729.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Cakmak A. Analysis of nonlinear Darcy-Forchheimer flows in porous media. [Thesis]. Texas Tech University; 2009. Available from: http://hdl.handle.net/2346/8729

Not specified: Masters Thesis or Doctoral Dissertation