(Springer, 2007) Arrarás Ventura, Andrés; Portero Egea, Laura; Jorge Ulecia, Juan Carlos; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
This work deals with the efficient numerical solution of nonlinear
transient flow problems posed on two-dimensional porous media of
general geometry. We first consider a spatial semidiscretization of such
problems by using a cell-centered finite difference scheme on a logically
rectangular grid. The resulting nonlinear stiff initial-value problems are
then integrated in time by means of a fractional step method, combined
with a decomposition of the flow domain into a set of overlapping subdomains
and a linearization procedure which involves suitable Taylor
expansions. The proposed algorithm reduces the original problem to the
solution of several linear systems per time step. Moreover, each one of
such systems can be directly decomposed into a set of uncoupled linear
subsystems which can be solved in parallel. A numerical example illustrates
the unconditionally convergent behaviour of the method in the
last section of the paper.