A new parallel implicit adaptive mesh refinement (AMR) algorithm is developed for the prediction of unsteady behaviour of laminar flames. The scheme is applied to the solution of the system of partial-differential equations governing time-dependent, two- and three-dimensional, compressible laminar flows for reactive thermally perfect gaseous mixtures. A high-resolution finite-volume spatial discretization procedure is used to solve the conservation form of these equations on body-fitted multi-block hexahedral meshes. A local preconditioning technique is used to remove numerical stiffness and maintain solution accuracy for low-Mach-number, nearly incompressible flows. A flexible block-based octree data structure has been developed and is used to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. The data structure also enables an efficient and scalable parallel implementation via domain decomposition. The parallel implicit formulation makes use of a dual-time-stepping like approach with an implicit second-order backward discretization of the physical time, in which a Jacobian-free inexact Newton method with a preconditioned generalized minimal residual (GMRES) algorithm is used to solve the system of nonlinear algebraic equations arising from the temporal and spatial discretization procedures. An additive Schwarz global preconditioner is used in conjunction with block incomplete LU type local preconditioners for each sub-domain. The Schwarz preconditioning and block-based data structure readily allow efficient and scalable parallel implementations of the implicit AMR approach on distributed-memory multi-processor architectures. The scheme was applied to solutions of steady and unsteady laminar diffusion and premixed methane-air combustion and was found to accurately predict key flame characteristics. For a premixed flame under terrestrial gravity, the scheme accurately predicted the frequency of the natural buoyancy induced oscillations. The performance of the proposed parallel implicit algorithm was assessed by comparisons to more conventional solution procedures and was found to significantly reduce the computational time required to achieve a solution in all cases investigated.

Zugl.: Erlangen, Nürnberg, Universiẗat, Diss., 2008.

Würzburg, Univ., Diss., 2008 / Zsfassung in dt. Sprache

Th. État--Philosophie--Paris, 1983. / Bibliogr. p. 366-375.

Thesis (M.S.)--Utah State University, 1971. / Title from title screen (viewed Aug. 14, 2009). Department: Wildlife Resources. Includes vita. Includes bibliographical references. Archival copy available in print.

Thesis (M. A.)--Trinity Evangelical Divinity School, Deerfield, Ill., 1998. / Abstract. Includes bibliographical references (leaves 262-272).

Dissertation (Ph.D.)--Worcester Polytechnic Institute. / Keywords: Periodic Solutions, Under-Determined Systems, Continuation, Nonlinear Eigenvalue, Inexact Newton Methods, Newton's Method, Trust Region Methods Includes bibliographical references (p.93-95).

Düsseldorf, Universiẗat, Diss., 2001.

Texte remanié de: Diss.--Tübingen Univ., 1990. / Notes bibliogr. p. 190-191. Index.

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 2012-10-21T15:12:44Z (GMT). No. of bitstreams: 1 221522.pdf: 893831 bytes, checksum: e0f7a25edf5c463738b416dc7b1239f0 (MD5) / O trabalho aqui presente destina-se a fazer uma análise comparativa, no contexo do método de Newton inexato, os desempenhos das metodologias iterativas baseadas em subespaços de Krylov: GMRES (Generalized Minimum Residual Method) e Bi-CGStab (Biconjugate Gradient Stabilized) e um método direto (LU esparso). As características das desempenhos (número de iterações e tempo computacional) das metodologias investigadas são acessadas com o uso de alguns testes padrão largamente utilizados como "benchmark" em mecânica dos fluidos computacional. O método de Newton inexato baseado em GMRES e Bi-CGStab é aplicado no sistema não linear gerado pelo método de elementos finitos (MEF) sobre o problema de valor de contorno composto pelas equações de Navier-Stokes. Uma importante observação diz respeito a condição necessária e suficiente de Brezzi-Babuka (ou condições inf-sup), a qual é satisfeita com o uso de parâmetros de estabilização.