3.6.2011

Jan Brezina:
Numerical coupling of Darcy flow on domains of different dimension

Abstract
Water in a granite rock is conducted by the complex system of fractures
of various sizes. In our approach the small fractures are modeled by an
equivalent permeable 3D continuum, while the preferential flow in the
substantial geological dislocations and their intersections is
considered as a flow on corresponding 2D manifolds and a flow on 1D
lines respectively. We shall present several physical models of the
coupling between dimensions and even more ways how to represent them on
the discrete level in the spirit of Mortar and XFEM methods. For
selected types of coupling, we shall show preliminary numerical tests of
convergence order. Finally, we shall put forward several open
theoretical questions and implementation issues that we are interested
in. These include: parallelism, computational geometry, advection-
diffusion-reaction equations, and discrete maximum principle.