%0 Thesis %1 citeulike:9678661 %A Barth, William L. %D 2004 %K imported %T Simulation of Non-Newtonian Fluids on Workstation Clusters %U http://gradworks.umi.com/31/43/3143367.html %X The subject of this work is the three-dimensional, parallel, finite element simulation on workstation clusters of coupled fluid flow and heat transfer of shear-thinning fluids modeled by the Powell-Eyring and extended Williamson models. After giving a description of the equations of motion and the numerical and computational techniques used to approximate them, the results of phenomenological studies for several different flow problems are presented. Of particular interest are nonlinear effects, multi-physics coupling, nonlinear instabilities, and multi-scale layer effects. First two internal pipe flow problems are presented to study the behavior of the fluid without the influence of thermal effects. The simulation of Poiseuille flow in a straight cylindrical pipe highlights the shear-thinning aspects of these fluids under a range of fluid parameters. This is followed by pressure-driven flow in a branched pipe where shear thinning may be seen toeffect the development of certain flow structures. The latter problem is of interest in traditional engineering pipe flows as well as biomedical engineer- ing applications such as blood flow treatment. We examine the detailed flow behavior in a branching zone. These studies are followed by two problems which are driven by temperature differences. The first is buoyancy-driven convection in an cube that was motivated by a benchmark challenge at CHT '01—the challenge was to provide definitive simulations and compare wit a prior experimental study. A detailed comparison of experimental and computational results for the Newtonian case was made and followed by an extension of the Newtonian problem to the non-Newtonian fluids considered here. The non-Newtonian fluids are shown to lead to higher heat fluxes across the domain with as the shear-thinning effect increases. This is followed by a surface-tension-driven convection problem in a fluid layer heated from below where experimental and computational results for the Newtonian case are compared with simulations of the Powell-Eyring and extended Williamson fluids. A dynamic matrix formation procedure based on a ” dial-an-operator” approach is also presented. This method uses a LaTeX-like input language for the specification of the governing equations to be solved. A parallel, structural incomplete LU factorization (SILU(0)) preconditioner which exploits the implicit structure of the zero-block in the matrices arising in incompressible flow problems is described. The preconditioner from one linear solution step is found to be ” reusable” in subsequent linear solution steps arising in thenon-linear iterative method and the time-stepping procedure. Finally, some performance analyses and scaling results are presented for the algorithms developed and implemented in the work on a broad range of workstation clusters. And the author's experience with cluster design, con- struction, and maintenance is described.

@phdthesis{citeulike:9678661, abstract = {{The subject of this work is the three-dimensional, parallel, finite element simulation on workstation clusters of coupled fluid flow and heat transfer of shear-thinning fluids modeled by the Powell-Eyring and extended Williamson models. After giving a description of the equations of motion and the numerical and computational techniques used to approximate them, the results of phenomenological studies for several different flow problems are presented. Of particular interest are nonlinear effects, multi-physics coupling, nonlinear instabilities, and multi-scale layer effects. First two internal pipe flow problems are presented to study the behavior of the fluid without the influence of thermal effects. The simulation of Poiseuille flow in a straight cylindrical pipe highlights the shear-thinning aspects of these fluids under a range of fluid parameters. This is followed by pressure-driven flow in a branched pipe where shear thinning may be seen toeffect the development of certain flow structures. The latter problem is of interest in traditional engineering pipe flows as well as biomedical engineer- ing applications such as blood flow treatment. We examine the detailed flow behavior in a branching zone. These studies are followed by two problems which are driven by temperature differences. The first is buoyancy-driven convection in an cube that was motivated by a benchmark challenge at CHT '01—the challenge was to provide definitive simulations and compare wit a prior experimental study. A detailed comparison of experimental and computational results for the Newtonian case was made and followed by an extension of the Newtonian problem to the non-Newtonian fluids considered here. The non-Newtonian fluids are shown to lead to higher heat fluxes across the domain with as the shear-thinning effect increases. This is followed by a surface-tension-driven convection problem in a fluid layer heated from below where experimental and computational results for the Newtonian case are compared with simulations of the Powell-Eyring and extended Williamson fluids. A dynamic matrix formation procedure based on a ” dial-an-operator” approach is also presented. This method uses a LaTeX-like input language for the specification of the governing equations to be solved. A parallel, structural incomplete LU factorization (SILU(0)) preconditioner which exploits the implicit structure of the zero-block in the matrices arising in incompressible flow problems is described. The preconditioner from one linear solution step is found to be ” reusable” in subsequent linear solution steps arising in thenon-linear iterative method and the time-stepping procedure. Finally, some performance analyses and scaling results are presented for the algorithms developed and implemented in the work on a broad range of workstation clusters. And the author's experience with cluster design, con- struction, and maintenance is described.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Barth, William L.}, biburl = {https://www.bibsonomy.org/bibtex/26a5a80ea83d07e98b97e1dd7e3a86e2b/gdmcbain}, citeulike-article-id = {9678661}, citeulike-linkout-0 = {http://gradworks.umi.com/31/43/3143367.html}, comment = {(private-note)cited by Barth \& Carey (2007)}, interhash = {73b2a46907cef2bd676763ce37c5bb24}, intrahash = {6a5a80ea83d07e98b97e1dd7e3a86e2b}, keywords = {imported}, posted-at = {2011-08-18 02:24:51}, priority = {2}, school = {The University of Texas at Austin}, timestamp = {2017-06-29T07:13:07.000+0200}, title = {Simulation of Non-{N}ewtonian Fluids on Workstation Clusters}, url = {http://gradworks.umi.com/31/43/3143367.html}, year = 2004 }