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- W4254873315 abstract "Publisher SummaryThis chapter presents the numerical solution of first-order hyperbolic problems in one dependent variable. Several simple difference equations are considered and examined for stability and truncation error. An understanding of the behavior of the simple difference equations lead to an improved understanding of some of the problems associated with the numerical solution of multiphase flow problems. There is a connection between stability and numerical dispersion, and the numerical dispersion acts to stabilize the difference equation. Example calculations indicate that a numerical solution of the diffusion–convection equation can exhibit numerical dispersion or some oscillatory behavior. The examples and truncation analyses apply only to the linearized version of the diffusion–convection equation; the same phenomena can be observed for nonlinear versions associated with multiphase flow. The user of a reservoir simulator needs to be aware that either numerical dispersion or oscillatory behavior can be expected in convection-dominated problems and that he can tradeoff between one and the other by adjusting the weighting factors." @default.
- W4254873315 created "2022-05-12" @default.
- W4254873315 date "1977-01-01" @default.
- W4254873315 modified "2023-09-27" @default.
- W4254873315 title "Chapter 4 Numerical Solution of First-Order Hyperbolic Problems in One Dependent Variable" @default.
- W4254873315 doi "https://doi.org/10.1016/s0376-7361(08)70237-1" @default.
- W4254873315 hasPublicationYear "1977" @default.
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