A note on approximate benchmark solutions for viscous two-layer flows

Mathieu Sellier, Richard Lenz

Abstract


An important test of the quality of numerical methods developed to track the interface between two fluids is their ability to reproduce test cases or benchmarks. However, benchmark solutions are scarce and virtually nonexistent for complex geometries. We propose a simple method to generate benchmark solutions in the context of the two-layer flow problem, a classical multiphase flow problem. The solutions are obtained by considering the inverse problem of finding the required channel geometry to obtain a prescribed interface profile. This viewpoint shift transforms the problem from that of having to solve a complex differential equation to the much easier one of finding the roots of a quartic polynomial.

doi:10.1017/S144618111000091X

Keywords


multiphase flow; long wave approximation; exact solution



DOI: http://dx.doi.org/10.21914/anziamj.v51i0.2769



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.