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

  • from Part I - Grid Generation, Discretizations, and Solvers
  • Edited by Knut-Andreas Lie, Olav Møyner
  • Book:
    Advanced Modeling with the MATLAB Reservoir Simulation Toolbox
    Published online:
    20 November 2021
    Print publication:
    25 November 2021, pp 46-69
    • Chapter
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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.