Desempenho de esquemas numéricos na modelagem da não linearidade da precipitação em um modelo atmosférico simplificado

• Autor(a) principal: Moita, Daniel Menon Simões
• Data de Publicação: 2011
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/159
• topic: Análise numérica; Soluções numéricas; Equações diferenciais parciais; Differential equations, Partial.; Numerical analysis; Numerical solutions; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA::ANALISE NUMERICA

The interaction between large-scale ux fields and precipitation fields in the tropical atmosphere can produce sharp boundaries between dry and humid regions (limited ahead by the rainfall front). As the speed of propagation of disturbances in these regions are di_erent, they form a discontinuity (Days and Pauluis, 2009). This phenomenon can be represented by a system of equations formed by the shallow water equations and the conservation equation of water vapor coupled by a nonlinear source term (Frierson et al., 2004). The aim of this study is to compare the consistency of results and performance of numerical simulation models that use ten di_erent numerical methods for solving these equations, including the finite di_erence methods: Leapfrog, Lax-Wendro_ and Leapfrog with _lters; the upwind method developed by Walcek (2000) and used in Freitas et al. (2011); and the finite volume methods: Godunov, Lax-Wendro_, Minmod, MC, Superbee and Bean-Warming. These models are tested with nonlinear conditions and, at the end, the results show that, albeit more complex and with a higher computational cost in identical simulations, the finite volume method is more appropriate to simulate such a phenomenon because it provides a more accurate solution when dealing with these discontinuities, thereby producing more realistic results than in the other cases. These results may have impact on the design of new models for the operational centers of weather and climate.