Not available / text

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Jan. 13, 2009). PDF text: v, 128 p. : col. ill. ; 2 Mb. UMI publication number: AAT 3315327. Includes bibliographical references. Also available in microfilm and microfiche formats.

Dresden, Techn. Univ., Diss., 1999.

Inaug.-Diss.--Rheinische Friedrich-Wilhelms-Universität zu Bonn, 1986. / Publication date on cover: 1987. Includes bibliographical references (p. 119-121).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Mary F. Wheeler. Vita. Includes bibliographical references.

Zugl.: Chemnitz, Techn. Univ., Diss., 2007 / Hergestellt on demand

Moment methods from the kinetic theory of gases exist as an alternative to the Navier-Stokes model. Models in this family are described by first-order hyperbolic PDEs with local relaxation. They provide a natural treatment for non-equilibrium effects and expand the regime for which the model is physically applicable past the Navier-Stokes level (when the continuum assumption breaks down). Discontinuous-Galerkin (DG) methods are very well suited for distributed parallel solution of first-order PDEs. This is because the optimal locality of the method minimizes needed communication between computational processes. One highly efficient, coupled space-time DG method that achieves third-order accuracy in both space and time while using only linear elements is the discontinuous-Galerkin Hancock (DGH) scheme, which was specifically designed for the efficient solution of PDEs resulting from moment closures. Third-order accuracy is obtained through the use of a technique originally proposed by Hancock. The combination of moment methods with the DGH discretization leads to a very efficient numerical treatment for viscous compressible gas flows that is accurate both in and out of local thermodynamic equilibrium. This thesis describe the first-ever implementation of this scheme for the solution of moment equations on large-scale distributed-memory computers. This implementation uses solution-directed automatic mesh refinement to increase accuracy while reducing cost. A linear hyperbolic-relaxation equation is used to verify the order of accuracy of the scheme. Next a supersonic compressible Euler case is used to demonstrate the mesh refinement as well as the scheme’s ability to capture sharp discontinuities. Third, a moment-closure is then used to compute a viscous mixing layer. This serves to demonstrate the ability of the first-order PDEs and the DG scheme to efficiently compute viscous solutions. A moment-closure is used to compute the solution for Stokes flow past a circular cylinder. This case reinforces the hyperbolic PDEs’ ability to accurately predict viscous phenomena. As this case is very low speed, it also demonstrates the numerical technique’s ability to accurately solve problems that are ill-conditioned due to the extremely low Mach number. Finally, the parallel efficiency of the scheme is evaluated on Canada’s largest supercomputer. It may be surprising to some that viscous flow behaviour can be accurately predicted by first-order PDEs. However, the applicability of hyperbolic moment methods to both continuum and non-equilibrium gas flows is now well established. Such a first-order treatment brings many physical and computational advantages to gas flow prediction.

Tese (Doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico. / Made available in DSpace on 2012-10-17T11:15:21Z (GMT). No. of bitstreams: 0Bitstream added on 2014-09-25T18:59:47Z : No. of bitstreams: 1 152592.pdf: 3613186 bytes, checksum: 905737fc0689d6078fb1c50cad3dab4b (MD5) / No presente trabalho é apresentada uma nova estratégia de adaptatividade p para a aproximação de Galerkin das equações integrais de contorno. Essa nova proposta é baseada no método hp-Clouds (Duarte, 1996), desenvolvido para os elementos finitos.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. Programa de Pós-Graduação em Matemática e Computação Científica. / Made available in DSpace on 2012-10-23T09:49:36Z (GMT). No. of bitstreams: 1 239022.pdf: 1476396 bytes, checksum: 41cf2b87fe43f24b6a31cf9e673e03ec (MD5) / Neste trabalho usaremos os métodos de Galerkin Descontínuo com Penalização Interior Simétrico e Não-Simétrico, para resolver problemas de Difusão-Advecção-Reação. Com base na aproximação obtida por esses métodos apresentamos estimativas a priori e a posteriori para o erro gerado ao usarmos esta aproximação em quantidades de interesse. As quantidades de interesse serão representadas por funcionais lineares limitados. Com base no indicador de erro obtido utilizando o resíduo e soluções do problema dual, apresentado nas estimativas a posteriori, apresentamos uma estratégia de adaptação do espaço de aproximação que procura melhorar as aproximações nas quantidades de interesse. Os experimentos numéricos comprovam as estimativas apresentadas, mostram a importância da consistência dual e ilustram o comportamento da estratégia adaptativa apresentada.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. Programa de Pós-Graduação em Matemática e Computação Científica. / Made available in DSpace on 2012-10-21T18:58:41Z (GMT). No. of bitstreams: 1 204406.pdf: 738799 bytes, checksum: f1a4d2417d7247d6d67901764d6ca357 (MD5) / Neste trabalho trataremos do método de Galerkin Descontínuo de Elementos Finitos para equações elípticas. Vamos apresentar definições e discussões de quatro variações do método de Galerkin Descontínuo e formular estimativas a priori de erro para três delas na norma de energia e em norma de L2. Com o intuito de comprovação das estimativas formuladas, trabalhamos com um exemplo destacando com gráficos a eficácia do método.