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Assessment of a Non-Conservative Four-Equation Multiphase System with Phase Transition

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Abstract

This work focuses on the formulation of a four-equation model for simulating unsteady two-phase mixtures with phase transition and strong discontinuities. The main assumption consists in a homogeneous temperature, pressure and velocity fields between the two phases. Specifically, we present the extension of a residual distribution scheme to solve a four-equation two-phase system with phase transition written in a non-conservative form, i.e. in terms of internal energy instead of the classical total energy approach. This non-conservative formulation allows avoiding the classical oscillations obtained by many approaches, that might appear for the pressure profile across contact discontinuities. The proposed method relies on a finite element based residual distribution scheme which is designed for an explicit second-order time stepping. We test the non-conservative residual distribution scheme on several benchmark problems and assess the results via a cross-validation with the approximated solution obtained via a conservative approach, based on a HLLC scheme. Furthermore, we check both methods for mesh convergence and show the effective robustness on very severe test cases, that involve both problems with and without phase transition.

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Acknowledgements

P. B. has been funded by the SNSF project grant \(\# 200021\_153604\).

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Author notes

  1. Paola Bacigaluppi

    Present address: Department of Aerospace Science and Technology, Politecnico di Milano, Milan, Italy

  2. Julien Carlier

    Present address: Institute of Mechanics, Materials and Civil Engineering, Université Catholique de Louain, Louvain-la-Neuve, Belgium

Authors and Affiliations

  1. Institute of Mathematics, University of Zurich, Zürich, Switzerland

    Paola Bacigaluppi & Rémi Abgrall

  2. ENSTA Paris, Institut Polytechnique de Paris, Palaiseau, France

    Julien Carlier & Marica Pelanti

  3. Inria, Centre des Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, France

    Pietro Marco Congedo

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  1. Paola Bacigaluppi
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Correspondence to Paola Bacigaluppi.

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Bacigaluppi, P., Carlier, J., Pelanti, M. et al. Assessment of a Non-Conservative Four-Equation Multiphase System with Phase Transition. J Sci Comput 90, 28 (2022). https://doi.org/10.1007/s10915-021-01706-6

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  • DOI: https://doi.org/10.1007/s10915-021-01706-6

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