Formulação de mínimos quadrados aplicada à problemas de escoamentos miscíveis - Fernandes, Kennedy Morais (2007)
Incompressible miscible flow in porous media which characterizes the process of tertiary recovery in oil reservoir are numerically solved in this work. Such flows are here modeled through a coupled nonlinear partial differential equations system with proper boundary and initial conditions. The mathematical model consists of an elliptic sub-system involving both pressure and velocity fields coming mass conservation law, Darcy's law and also from a transport equation, which is predominantly convective being to the concentration the main variable in this problem. Several variational formulation have been used to solve this problem aiming the determination of an accurate velocity field. In the present work finite element method with a least square variational formulation are applied to the elliptic sub-system considering also the inclusion of the null rotational equation which allow as to obtain H1 convergence both for pressure as well for the velocity approximations. The convection-diffusion equation is also numerically solved through least squares formulation after it has been rewritten as a first order system of differential equation. This formulation besides of its mixed character allows equal order interpolation for concentration and for it derivative. Numerical results are presented and compared to the ones showed in the open literature.