Solving one-dimensional two-phase flow problems in rigid porous media using L-scheme

Resumo

This work aims to obtain the numerical solution for one-dimensional two-phase flow in rigid porous
media. The mathematical model for the problem consists of a system of partial differential equations with a set
of algebraic relations using the pressure-pressure formulation based on L-scheme linearization. The finite volume
method (FVM) is used to discretize the system of partial differential equations in a uniform grid. The spatial
approximation is obtained by the second-order scheme (CDS) and the temporal approximation by the implicit
Euler method. Dirichlet boundary conditions are applied. Iterative methods are used to solve the resulting system
of algebraic equations. A study on L-scheme was carried out to establish a rule and value of L that guarantees the
convergence of this linearization method. The results obtained for the numerical problem are compared with those
of a problem with the same characteristics in the literature that uses the pressure-saturation formulation.