This study describes the numerical solution and computational implementation of the isothermal transient flow of several different compressible liquids contained in a single elastic pipeline. The method of characteristics is used to integrate the equations of conservation of mass and momentum along the deforming Eulerian characteristic mesh. Integration along the deforming mesh, which is generated as integration proceeds in time, minimizes the need for interpolation so that problem variables are accurately determined at the computed mesh points. On the other hand, since calculated mesh points are not regularly spaced in the x-t plane, interpolations among the computed points become necessary to find the value of variables at a given fixed instant of time along the length of the pipeline. The computational implementation allows for the simulation of flow across locations where there may be changes in nominal pipe diameter, valves or pumps, as well as tracking the position of fluid interfaces as different batches of fluid move along the pipeline, and results are found to be numerically accurate and stable.

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