A finite volume discretization of the incompressible two-fluid model in four-equation form is proposed for simulating roll waves appearing in multiphase pipelines. The new formulation has two important advantages compared to existing roll wave simulators: (i) it is conservative by construction, meaning that the correct shock magnitude is obtained at the hydraulic jump, and (ii) it can be more easily extended with additional physics (e.g. Compressibility, axial diffusion, surface tension), without rederiving the model equations. A simple, robust, first-order upwind discretization of the four-equation model is able to capture the roll wave profiles, although a fine grid is needed to achieve converged results. The four-equation model leads to new roll wave solutions that differ from existing analytical and numerical results. Our solutions are believed to be physically more correct because the shock relations satisfy physically conserved quantities.

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Conference North American Conference on Multiphase Production Technology
Sanderse, B, Misra, S, Dubinkina, S, Henkes, R.A.W.M, & Oosterlee, C.W. (2018). Numerical simulation of roll waves in pipelines using the two-fluid model. In 11th North American Conference on Multiphase Technology (pp. 373–386).