Annette Stephansen
Centre for Integrated Petroleum Research
University of Bergen
Bergen, Norway
The multi point flux approximation (MPFA) is a control volume method
developed by the oil industry as a reliable discretization of the
pressure equation, derived from Darcy's law, on general rough
grids. In reservoir simulation the geology of the reservoir, which
includes faults and non parallel layers in the media, is a major
challenge. The particularity of the MPFA method is its ability to
provide a local explicit flux with respect to the pressure, which
allows for a fully implicit multiphase simulation.
The analysis of the multi point flux approximation (MPFA) method has
so far relied on the possibility of seeing it as a mixed finite
element method for which the convergence is then established. This
type of analysis has been successfully applied to triangles and
quadrilaterals, lately also in the case of rough meshes.
Another well known conservative method, the mimetic finite difference
method, has also traditionally relied on the analogy with a mixed
finite element method to establish convergence. Recently however a new
type of analysis proposed by Brezzi, Lipnikov and Shashkov permits to
show convergence of the mimetic method on a general polyhedral mesh.
Formulating the MPFA O-method in a mimetic finite difference
framework it is possible to extend the convergence proof of the MPFA
method to general polyhedral meshes. We examine the limitations of the proof
linked to the general non-symmetry of the MPFA method.