Avaliação dos algoritmos de Picard-Krylov e Newton-Krylov na solução da equação de Richards

• Autor(a) principal: Guterres, Marcelo Xavier
• Data de Publicação: 2013
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13672
• topic: Richards equation; Picard-Krylov; Newton-Krylov; PETSc; Dinâmica dos fluidos Modelos matemáticos; Método dos volumes finitos; Equações diferenciais parciais; Permeabilidade Modelos matemáticos; Newton-Krylov, Método; Picard-Krylov, Método; Fluidodinâmica computacional; Richards, Equação de; PETSc; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES

Geotechnical Engineering is the area of Civil Engineering that studies the interaction between constructions carried out by man or natural phenomena with geological environment, which most of times is partially saturated soil. In this sense, work developing as stabilization, dam containing, retaining walls, foundations and highways are conditioned to a right prediction of water flow into the soil. However, considering the water flow, the studied region areas are commonly on the order of square kilometers, mathematical models solutions require computational meshes of large proportions, causing serious limitations linked to computational memory requirements and processing time. In order to overcome these limitations, efficient numerical methods must be used in the solution of the considered problem. Hence iterative methods for solving nonlinear and large sparse linear systems must be used in this type of application. In short, this study approached a solution to the Richard partial differential equation by the two dimensions finite volume method, bringing Picard and Newton method with greater efficiency. Linear system resolution iterative techniques based on Krylov space with pre-conditioners matrix were used. Portable Extensible Toolkit for Scientific Computation (PETSc) numerical library was a tool used during the task. The results indicate when a Richards equation is solved considering thr PICARD-KRYLOV method, no matter the soil evaluation model, the best combination for solving linear systems is the stabilized double gradient method and the SOR preconditioning. On the other hand, when the van Genuchten equations are used the gradients methods with the SOR preconditioning must be chosen. Adopting the NEWTON-KRYLOV method, the stabilized double gradient method is more efficient in soling Newton linear system, in relation to the preconditioning it must be giving preference to the Jacob block. Finally, there are strong indications that the PICARDKRYLOV method can be more effective than the NEWTON-KRYLOV one, when used for solving Richards partial differential equation.