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6 - Consistent Discretizations on Polyhedral Grids

from Part II - Single-Phase Flow

Published online by Cambridge University Press:  22 July 2019

Knut-Andreas Lie
Affiliation:
SINTEF, Norway
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Summary

The two-point flux-approximation (TPFA) scheme is robust in the sense that it generally gives a linear system that has a solution regardless of the variations in K and the geometrical and topological complexity of the grid. The resulting solutions will also be monotone, but the scheme is only consistent for certain combinations of grids and permeability tensors K. This implies that a TPFA solution will not necessarily approach the true solution when we increase the grid resolution. It also means that the scheme may produce different solutions depending upon how the grid is oriented relative to the main flow directions. In this chapter, we first explain the lack of consistency for TPFA, before we introduce a few consistent schemes implemented in MRST, including the mimetic finite-difference method and one example of a multipoint flux approximation method (MPFA-O). These can all be written on a general mixed hybrid form, which is motivated by mixed finite-element methods. We explain how you can specify different methods that reduce to known methods on simple grids by adjusting the inner product in the mixed hybrid formulation.

Type
Chapter
Information
An Introduction to Reservoir Simulation Using MATLAB/GNU Octave
User Guide for the MATLAB Reservoir Simulation Toolbox (MRST)
, pp. 174 - 201
Publisher: Cambridge University Press
Print publication year: 2019
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC-ND 4.0 https://creativecommons.org/cclicenses/

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