Análise de um método para equação de convecção formulado à luz da mecânica dos meios contínuos a advecção de anomalias oceânicas e meteorológicas / Analysis of a method for the convection equation formulated in the light of mechanical means of the continuous advection of oceanic and meteorological anomalies

AUTOR(ES)
DATA DE PUBLICAÇÃO

2006

RESUMO

In the present work we studied and analyzed the Trajectories Tube method, a conservative, explicit, simple, physically intuitive, semi-Lagrangian algorithm for the convection equation. Kinematical aspects of the mechanics of continuous media are essentially the tools used for formulation and feasibility analysis. We showed that this method is unconditionally stable, essentially nondispersive, convergent and accurate of order two in time and space. Computational experiments with non-isochoric and isochoric motions show that the studied method can be used in compressible and incompressible flow. Numerical solutions of systems of ordinary differential equations (necessary conditions for acomplishment of the scheme) are tested in the Trajectories Tube method context, with classical difficult examples. Applications are considered in the ambit of oceanic transport and advection of atmospheric fronts, including the tracer problem within a Stommel gyre and the computation of the Dowell frontogenesis. Comparisions with other methodologies show the superiority of the Trajectories Tube method.

ASSUNTO(S)

algoritmo semi-lagrangiano transporte oceânico matematica aplicada circulações oceânicas differential equations - numerical solutions equação de convecção ocean circulation oceanic transport método do tubo de trajetórias convection equation lagrange equations numerical analysis equações diferenciais - soluções numéricas frente (meteorologia) semi-lagrangian algorithm análise numérica fronts (meteorology) mecânica dos meios contínuos lagrange, equações de mechanics of continua trajectories tube method

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