Journal Article10.1061/(ASCE)0733-9429(1983)109:5(670)
Characteristics Method Using Time‐Line Interpolations
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TL;DR: In this paper, two time-line interpolations are presented and analyzed in the solution of a linearized water hammer problem, and error analysis and numerical experiments demonstrate the degree of damping and dispersion introduced by both reachback and implicit timeline interpolation methods.
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Abstract: The use of interpolations in time, rather than the more widely used spatial interpolations, demonstrates several benefits in the application of the method of characteristics to wave problems in hydraulics. Two such time-line schemes are presented and analyzed in the solution of a linearized water hammer problem. Reachback time-line interpolations, where the characteristic lines are projected back before the current time step, demonstrate less damping than the corresponding spatial interpolation scheme at the same discretization. Implicit time-line interpolations, where the characteristic line is projected into the current time step, permit relaxation of the restrictive time step required by the Courant condition. An error analysis and numerical experiments demonstrate the degree of damping and dispersion introduced by both reachback and implicit time-line interpolation methods. The error analyses and their verification may encourage further application of these methods in appropriate problem domains.
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Citations
A Review of Water Hammer Theory and Practice
TL;DR: In this paper, the authors present an overview of both historic developments and present research and practice in the field of hydraulic transients, including mass and momentum equations for one-dimensional flows.
760
Systematic Evaluation of One-Dimensional Unsteady Friction Models in Simple Pipelines
TL;DR: In this article, basic unsteady flow types and transient event types are categorized, and then the same authors test two different models for each type of transient event, i.e., the constant coefficient instantaneous acceleration-based model and the convolution based model, against experimental data from a laboratory pipeline.
Analysis of Liquid and Structural Transients in Piping by the Method of Characteristics
TL;DR: In this paper, the authors proposed a mathematical model for predicting the liquid pressure and pipe stress responses to transient excitation of either liquid or piping, which can be described as one-dimensional wave phenomena.
154
Godunov-Type Solutions for Water Hammer Flows
Ming Zhao,Mohamed Salah Ghidaoui +1 more
TL;DR: In this paper, first-and second-order explicit finite volume (FV) Godunov-type schemes for water hammer problems are formulated, applied, and analyzed for Courant numbers less than or equal to one.
139
References
Fixed-Grid Characteristics for Pipeline Transients
TL;DR: In this article, the authors used linear interpolations along time lines to predict pipeline transients and showed the effects of interpolation, spacing, and grid size on numerical attenuation and dispersion.
70
Comparison of Four Numerical Methods for Flood Routing
TL;DR: In this article, the authors compared the accuracy and efficiency of four of the more important numerical methods for flood routing by simulating the propagation of the monoclinal wave in two channels with different bottom slopes, and showed that the implicit method of Amein is in general the most suitable method for routing floods in rivers of small slope.
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