  The paper is devoted to the derivation, by linearization, of simplified
(fully homogenized) homogenized models of an immiscible incompressible
two-phase flow in double porosity media in the case of thin fissures. In a
simplified dual porosity model derived previously by the authors the
matrix-fracture source term is approximated by a convolution type source term.
This approach enables to exclude the cell problem, in form of the imbibition
equation, from the global double porosity model. In this paper we propose a new
linear version of the imbibition equation which leads to a new simplified dual
porosity model. We also present numerical simulations which show that the
matrix-fracture exchange term based on this new linearization procedure gives a
better approximation of the exact one than the corresponding exchange term
obtained earlier by the authors.

Analysis of PDEs