Investigações sobre um esquema numérico desacoplado para modelos de circulação

Abstract

The numerical modelation by the means of finite elements can represent the frontiers of an irregular water body more eficiently than those models employing finit differences. However, finit differences models are usually solved through highly efficient algorithims, such as the ADI (Alternate Direction Implicit). Through an uncoupling in the calculation of the multiple variables (e.g. water level elevation, velocity components, salinity, etc ... ) it is possible to reduce the problem to multiple solutions of tridiagonal systems. Such algoritims, unfortunatly, are not useful in the case of finit elements, what increases its computational costs. The present thesis proposes a numerical algoritm which solves the equations of movement by making successive substitutions in the continuity equation, allowing uncoupling, even for finite elements, with great efficiency. The results of the preliminary investigation are presented, in which, in order to test the algorithim feasibility, two finite differences models for the simulation of the flow conditions in tidal canals were used, based on a one dimensional mathematics formulation. One of them solves the governant equations in an coupled way, and the other uses the proposed uncoupled algorithim. More rigorous numerical stability conditions were then verified in using the un-coupled model, but specifically in the simulations of extreme cases (with Courrant number already highly valued). For usual simulation conditions, the uncoupled model proposed was almost effectively equivalent to the conventional coupled model, concerning both, numerical process and results' precision.Such results allow the cautelous prevision of excelent possibilities concerning the extension of this technique to multidimensional circulation models, even using finite elements algorithims, leading to a significant economy of memory space and processing time.