Running count methods for solving the tasks of water hammer
UDC: 658.264.003.13
DOI: -
Authors:
SIDLER INNA V.
1
1 Melentiev Energy Systems Institute SB RAS, Irkutsk, Russia
Keywords: water hammer, pipeline, system of partial differential equations of hyperbolic type, numerical methods
Annotation:
Practical applications of pipeline and hydraulic systems require the creation of transient processes efficient models in pipelines and the development of high-speed numerical methods that will allow reducing the duration of machine calculations without loss of accuracy. The author of the article presents the water hammer mathematical model as a mixed problem for a nonlinear system of hyperbolic differential equations. For the numerical solution of the problem, a running count difference method is proposed, which takes into account the specifics of the equations and boundary conditions of the problem. An analytical example is constructed that looks like the problem under study. Based on it, the effectiveness of the proposed explicit and implicit numerical schemes of running counting is compared with the method of characteristics, which is traditionally used for practical calculations related to the occurrence of water hammer. The stable behavior of the solution obtained using the implicit running count method with a large time step is shown, which made it possible to reduce the duration of machine calculations compared with the characteristics method and the explicit running count scheme. The results of calculations for the task of water hammer with real parameters are presented.
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