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Computational Model for Compressible Two-Phase Flow in Deformed Porous Medium

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Computational Science and Its Applications – ICCSA 2021 (ICCSA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12949))

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Abstract

A new three-phase model of compressible two-fluid flows in a deformed porous medium is presented. The derivation of the model is based on the application of the Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems theory to three-phase solid-fluid mixture. The resulting governing equations are hyperbolic and satisfy the laws of irreversible thermodynamics - conservation of energy and growth of entropy. Due to these properties, the formulated model is well suited for the straightforward application of advanced high accuracy numerical methods applicable to the solution of hyperbolic systems, and ensures the reliability of the numerically obtained solutions. On the basis of the formulated nonlinear model, the governing equations for the propagation of small-amplitude waves are obtained, allowing the use of an efficient finite-difference scheme on staggered grids for their numerical solution. Some numerical examples are presented showing the features of wave propagation in a porous medium saturated with a mixture of liquid and gas with their different ratios.

The work is supported by Mathematical Center in Akademgorodok, the agreement with Ministry of Science and High Education of the Russian Federation number 075-15-2019-1613. I.P. also acknowledge funding from the Italian Ministry of Education, University and Research (MIUR) under the Departments of Excellence Initiative 2018–2022 attributed to DICAM of the University of Trento (grant L. 232/2016), as well as financial support from the University of Trento under the Strategic Initiative Modeling and Simulation. I.P. has further received funding from the University of Trento via the UniTN Starting Grant initiative.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Novosibirsk, 630090, Russia

    Evgeniy Romenski, Galina Reshetova & Ilya Peshkov

  2. Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, 630090, Russia

    Galina Reshetova

  3. Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, Trento, Italy

    Ilya Peshkov

Authors
  1. Evgeniy Romenski
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  2. Galina Reshetova
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  3. Ilya Peshkov
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Corresponding author

Correspondence to Evgeniy Romenski .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Monash University, Clayton, VIC, Australia

    David Taniar

  7. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

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Romenski, E., Reshetova, G., Peshkov, I. (2021). Computational Model for Compressible Two-Phase Flow in Deformed Porous Medium. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_16

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  • DOI: https://doi.org/10.1007/978-3-030-86653-2_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86652-5

  • Online ISBN: 978-3-030-86653-2

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