Non-equilibrium Model for Weakly Compressible Multi-component Flows: The Hyperbolic Operator

Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


We present a novel pressure-based method for weakly compressible multiphase flows, based on a non-equilibrium Baer and Nunziato-type model. Each component is described by its own thermodynamic model, thus the definition of a mixture speed of sound is not required. In this work, we describe the hyperbolic operator, without considering relaxation terms. The acoustic part of the governing equations is treated implicitly to avoid the severe restriction on the time step imposed by the CFL condition at low-Mach. Particular care is taken to discretize the non-conservative terms to avoid spurious oscillations across multi-material interfaces. The absence of oscillations and the agreement with analytical or published solutions is demonstrated in simplified test cases, which confirm the validity of the proposed approach as a building block on which developing more accurate and comprehensive methods.


Non-equilibrium multiphase flows Low-mach scheme Diffuse interface methods 



This publication has been produced with support from the NCCS Centre, performed under the Norwegian research program Centres for Environment-friendly Energy Research (FME). The authors acknowledge the following partners for their contributions: Aker Solutions, Ansaldo Energia, CoorsTek Membrane Sciences, Emgs, Equinor, Gassco, Krohne, Larvik Shipping, Norcem, Norwegian Oil and Gas, Quad Geometrics, Shell, Total, Vår Energi, and the Research Council of Norway (257579/E20).


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© Springer International Publishing AG 2020

Authors and Affiliations

  1. 1.Institute of MathematicsUniversität ZürichZürichSwitzerland

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