L-scheme and modified Picard with multigrid method for a 1D two-phase problem in rigid porous media with analytical solution
Palavras-chave:
Two-phase flow, Linearization methods, Coupled problem, Finite Volume Method, Implicit EulerResumo
Applications of two-phase problems in porous media are common in Geomechanics, Hydrogeology,
Engineering and Biomedicine. There are different formulations when working on two-phase problems, in this
work we have chosen to use the pressure-pressure formulation. The equations system generated is a strongly non-
linear system of coupled partial differential equations. Thus, the modified Picard and L-scheme to perform its
linearization, the Finite Volume Method for the discretization of the equation in space and implicit Euler scheme
for the discretization of the equation in time were used. The systems of linear equations generated were solved
by the lexicographic Gauss-Seidel solver in a coupled way. In this work, we proposed to use multigrid method
with the Correction Scheme and W-cycle, in order to accelerate the convergence of this solver. Based on the tests
performed using an example with a known analytical solution, it was possible to notice the convergence to the
solution with a few iterations and little computational time.
