Application of a heterogenous multiscale method to multi-batch driven pipeline

The problem of simulating pipelines that are used for transporting different fluids is addressed in the paper. The model of the multi-batch pipeline is obtained by extending the classical “water hammer equations” (dealing with pressure and velocity of the medium) with fluid density. In such way a system of nonlinear partial differential equations is derived and solved by the method of characteristics. However, the ordinary differential equations resulting from the method of characteristics are defined on domains with very different slopes in the (x,t) space. A heterogenous multiscale method using two grids is capable of coping with associated numerical problems as shown by comparison of simulated and measured data on a real pipeline.