Aplicação da Técnica de Redução de Ordem em Elementos Finitos para Simulações de Fluxo Transiente em Aquíferos.

Resumo

Aquifers are geological formations whose water extraction has guaranteed the supply of populations
worldwide. The management of this type of system composed of porous rocks aims at both longevity of the natural
resource and security of the extraction. Management is carried out through the solution of flow equation that
represents the balance between water extraction (represented mainly by production wells) and aquifer recharge.
The flow equation is a partial differential equation whose unknown is the hydraulic head and can be solved through
numerical methods such as the finite difference method and the finite element method. In this modeling, a high
level of discretization is required in order to have a reliable description of the permeability and porosity fields,
fundamental properties that respectively control the flow and storage of water in the pores of the rock. At the same
time, the aquifer is a very extensive domain (on the kilometer scale), thereby generating numerical models with
high degrees of freedom.
In this type of problem, techniques that promote the reduction of the number of degrees of freedom, without
considerable loss of the quality of the solution, can be extremely useful, especially when combined with
uncertainty or optimization analysis, which require a large number of water flow simulations at aquifer scale. In
this context, this paper discusses and proposes methodologies for reducing the model order of the water flow
problem in aquifers solved by the finite element method.