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Non-equilibrium model for weakly compressible multi-component flows: The hyperbolic operator


Re, Barbara; Abgrall, Rémi (2020). Non-equilibrium model for weakly compressible multi-component flows: The hyperbolic operator. In: di Mare, Francesca; Spinelli, Andreas; Pini, Matteo. Non-Ideal Compressible Fluid Dynamics for Propulsion and Power. Cham: Springer, 33-45.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Book Section, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Automotive Engineering
Physical Sciences > Aerospace Engineering
Physical Sciences > Mechanical Engineering
Physical Sciences > Fluid Flow and Transfer Processes
Language:English
Date:1 January 2020
Deposited On:15 Dec 2020 12:41
Last Modified:31 Jan 2021 14:04
Publisher:Springer
Series Name:Lecture Notes in Mechanical Engineering
Number:NICFD 2018
ISSN:2195-4364
ISBN:9783030496258
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/978-3-030-49626-5_3

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