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1 results

  • 9 - Discretizing Hyperbolic Transport Equations

  • from Part III - Multiphase Flow
  • Knut-Andreas Lie
  • Book:
    An Introduction to Reservoir Simulation Using MATLAB/GNU Octave
    Published online:
    22 July 2019
    Print publication:
    08 August 2019, pp 272-288
    • Chapter
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  • Summary

    The chapter discusses numerical discretization of first-order quasilinear hyperbolic PDEs, so-called conservation laws. We start by briefly reviewing some of the theory for these equations, including weak solutions, discontinuities, and entropy conditions. We then present a general family of conservative finite-volume methods that includes centered as well as upwind and Godunov-type schemes. We demonstrate typical deficiencies in classical schemes including smearing of discontinuities and creation of nonphysical oscillations. We end the chapter by presenting the implicit, upstream-mobility scheme, which is the most widespread method in reservoir simulation.