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2 - Nonlinear Finite-Volume Methods for the Flow Equation in Porous Media

from Part I - Grid Generation, Discretizations, and Solvers

Published online by Cambridge University Press:  20 November 2021

By
Mohammed Al Kobaisi  and
Wenjuan Zhang
Edited by
Knut-Andreas Lie  and
Olav Møyner
Knut-Andreas Lie
Affiliation:
SINTEF
Olav Møyner
Affiliation:
SINTEF
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Summary

This chapter explains how one can formulate nonlinear finite-volume (NFV) methods, as advanced discretization schemes, to solve the flow equation in porous media. These schemes are of particular interest because apart from being consistent, they are monotone by design. We explain the basic ideas of the NFV methods: how to construct one-sided fluxes, interpolate using harmonic averaging points, and obtain unique discrete fluxes through grid faces with convex combinations of one-sided fluxes. We outline key functions in the accompanied nfvm module in the MATLAB Reservoir Simulation Toolbox (MRST) and show some examples of how the method is applied.

Keywords

consistent discretizationfinite volumepermeability tensor nonlinear two-point approximation (NTPFA)nonlinear multipoint flux approximation (NMPFA)harmonic averaging pointinterpolationone-sided fluxconvex combinationlinearity-preserving discrete maximum principle monotonicity positivity preserving
Type
Chapter
Information
Advanced Modeling with the MATLAB Reservoir Simulation Toolbox , pp. 46 - 69
Publisher: Cambridge University Press
Print publication year: 2021
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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