Abstract
Multiphase flow in fractured porous media can be described
by discrete fracture matrix models that represent the fractures as
dimensionally reduced manifolds embedded in the bulk porous medium.
Generalizing earlier work on this approach we focus on immiscible
two-phase flow in time-dependent fracture geometries, i.e., the fracture
itself and the aperture of the fractures might evolve in time. For
dynamic fracture geometries of that kind, neglecting capillary forces,
we deduce by transversal averaging of a full dimensional description a
dimensionally reduced model that governs the geometric evolution and the
flow dynamics. The core computational contribution is a
mixed-dimensional finite-volume discretization based on a conforming
moving-mesh ansatz. This finite-volume moving-mesh (FVMM) algorithm is
tracking the fractures' motions as a family of unions of facets of the
mesh. Notably, the method permits arbitrary movement of facets of the
triangulation while keeping the mass conservation constraint. In a
series of numerical examples we investigate the modeling error of the
reduced model as it compares to the original full dimensional model.
Moreover, we show the performance of the finite-volume moving-mesh
algorithm for the complex wave pattern that is induced by the
interaction of saturation fronts and evolving fractures.
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