# A Mathematical Model for Nonstationary Liquid- Gas Mixture Flow in Pipelines

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## Abstract

In this paper a mathematical model for nonstationary liquid-gas mixture flow in pipelines is presented covering waterhammer and cavitation phenomena. The proposed model which is an initial-boundary value problem for hyperbolic sastem of conservation laws is then analysed. Charcteristic fields for the hyperbolic system are calculated and Riemann problem is solved using shock waves and rarefaction waves. For the numerical solution of the complete problem essentially nonoscillatory schemes are recommended.

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