An Analysis of Upstream Differencing
- 1 August 1988
- journal article
- Published by Society of Petroleum Engineers (SPE) in SPE Reservoir Engineering
- Vol. 3 (03) , 1053-1056
- https://doi.org/10.2118/14045-pa
Abstract
Summary: A complete convergence analysis is carried out for upstream differencing as applied to one-dimensional (ID) tilted reservoirs experiencing gravity-segregation effects and possible countercurrent flows. It is shown that the standard upstream method converges to the correct physical solution of this problem, provided that an appropriate stability condition holds. Results from the theory of monotone-difference schemes are used. It is concluded that in addition to the practical advantages of the upstream formulation, there is also a strong theoretical justification for use of upstream techniques in multidimensional reservoir simulation.Keywords
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