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A NOTE ON APPROXIMATE BENCHMARK SOLUTIONS FOR VISCOUS TWO-LAYER FLOWS

Part of: Two-phase and multiphase flows

Published online by Cambridge University Press:  10 February 2011

M. SELLIER  and
R. D. LENZ
M. SELLIER*
Affiliation:
Department of Mechanical Engineering, The University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand (email: [email protected])
R. D. LENZ
Affiliation:
ExxonMobil Research and Engineering, Fairfax, VA 22037, USA (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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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.

Keywords

multiphase flowlong wave approximationexact solution

MSC classification

Secondary: 76T99: None of the above, but in this section
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 4 , April 2010 , pp. 406 - 415
Copyright
Copyright © Australian Mathematical Society 2011

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