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A well-balanced numerical scheme for a model of two-phase flows with treatment of nonconservative terms

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Abstract

We construct a numerical scheme for a model of two-phase flows. The keystone is the treatment of nonconservative terms using stationary contact discontinuities. The nonconservative terms are absorbed into left-hand and right-hand states of the local stationary contact discontinuity at each grid node. The numerical scheme is built by taking into accounts the states on both sides of local contact discontinuities as supplemented facts of a standard numerical approximation for the conservative part of the system. The scheme is shown to possess interesting properties: it preserves the positivity of the volume fractions in both phases and the positivity of the gas density, it is well-balanced and satisfying the numerical minimum entropy principle in the gas phase.

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Acknowledgments

The author would like to thank the reviewers for their very constructive comments and fruitful discussions.

Funding

This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number B2018-28-01.

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Authors and Affiliations

  1. Department of Mathematics, International University, Vietnam National University-Ho Chi Minh City, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam

    Mai Duc Thanh

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  1. Mai Duc Thanh
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Correspondence to Mai Duc Thanh.

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Communicated by: Paul Houston

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Thanh, M.D. A well-balanced numerical scheme for a model of two-phase flows with treatment of nonconservative terms. Adv Comput Math 45, 2701–2719 (2019). https://doi.org/10.1007/s10444-019-09704-x

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  • DOI: https://doi.org/10.1007/s10444-019-09704-x

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