Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Analysis and simulation of a new multi-component two-phase flow model with phase transitions and chemical reactions


Authors: Maren Hantke and Siegfried Müller
Journal: Quart. Appl. Math. 76 (2018), 253-287
MSC (2010): Primary 76T30, 76T10, 74A15, 80A32, 82C26
DOI: https://doi.org/10.1090/qam/1498
Published electronically: January 18, 2018
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Abstract | References | Similar Articles | Additional Information

Abstract: A class-II-model for multi-component mixtures recently introduced in D. Bothe and W. Dreyer, Continuum thermodynamics of chemically reacting fluid mixtures, Acta Mech., 226 (2015), 1757-1805, is investigated for simple mixtures. Bothe and Dreyer were aiming at deriving physically admissible closure conditions. Here the focus is on mathematical properties of this model. In particular, hyperbolicity of the inviscid flux Jacobian is verified for non-resonance states. Although the eigenvalues cannot be determined explicitly but have to be computed numerically an eigenvector basis is constructed depending on the eigenvalues. This basis is helpful to apply standard numerical solvers for the discretization of the model. This is verified by numerical computations for two- and three-component mixtures with and without phase transition and chemical reactions.


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Additional Information

Maren Hantke
Affiliation: Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, PSF 4120, D-39016 Magdeburg, Germany
Email: maren.hantke@ovgu.de

Siegfried Müller
Affiliation: Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany
Email: mueller@igpm.rwth-aachen.de

DOI: https://doi.org/10.1090/qam/1498
Received by editor(s): May 23, 2017
Published electronically: January 18, 2018
Additional Notes: The authors are very grateful to the Mathematisches Forschungsinstitut Oberwolfach (MFO) for its hospitality and giving us the opportunity to spend four weeks at the MFO within the Research in Pairs programme.
Article copyright: © Copyright 2018 Brown University

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