Abstract
Relationships among various mass-conservative discretization techniques for equations of the type -Δ. Krp = q on distorted logically rectangular meshes are discussed. The case of heterogeneous, anisotropic K is important for applications to subsurface porous media, in particular the groundwater flow equation and the pressure equation of petroleum reservoir simulation. Some methods are based on K itself, others on K -1. Within one of these groups, mass lumping and quadrature can be keys to understanding connections between methods; incomplete inversion of the mass matrix is useful in relating one group to the other.
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Russell, T.F. (2000). Relationships among Some Conservative Discretization Methods. In: Chen, Z., Ewing, R.E., Shi, ZC. (eds) Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics, vol 552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45467-5_22
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DOI: https://doi.org/10.1007/3-540-45467-5_22
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