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Thermodynamically Compatible Hyperbolic Model for Two-Phase Compressible Fluid Flow with Surface Tension
- Authors: Romenski E.1, Peshkov I.2
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Affiliations:
- Sobolev Institute of Mathematics SB RAS
- University of Trento
- Issue: Vol 87, No 2 (2023)
- Pages: 211-225
- Section: Articles
- URL: https://journal-vniispk.ru/0032-8235/article/view/138853
- DOI: https://doi.org/10.31857/S0032823523020121
- EDN: https://elibrary.ru/UATYDZ
- ID: 138853
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Abstract
A two-phase flow model for compressible immiscible fluids is presented, the derivation of which is based on the use of the theory of symmetric hyperbolic thermodynamically compatible systems. The model is an extension of the previously proposed thermodynamically compatible model of compressible two-phase flows due to the inclusion of new state variables of the medium associated with surface tension forces. The governing equations of the model form a hyperbolic system of differential equations of the first order and satisfy the laws of thermodynamics (energy conservation and entropy increase). The properties of the model equations are studied and it is shown that the Young–Laplace law of capillary pressure is fulfilled in the asymptotic approximation at the continuum level.
Keywords
About the authors
E. Romenski
Sobolev Institute of Mathematics SB RAS
Author for correspondence.
Email: evrom@math.nsc.ru
Russia, Novosibirsk
I. Peshkov
University of Trento
Author for correspondence.
Email: ilya.peshkov@unitn.it
Italy, Trento
References
- Brackbill J.U., Kothe D.B., Zemach C. A continuum method for modeling surface tension // J. Comput. Phys., 1992, vol. 100, no. 2, pp. 335–354.
- Perigaud G., Saurel R. A compressible flow model with capillary effects // J. Comput. Phys., 2005, vol. 209, no.1, pp. 139–178.
- Popinet S. Numerical models of surface tension // Annu. Rev. Fluid Mech., 2018, vol. 50, no. 1, pp. 49–75.
- Schmidmayer K., Petitpas F., Daniel E., Favrie N., Gavrilyuk S. A model and numerical method for compressible flows with capillary effects // J. Comput. Phys., 2017, vol. 334, pp. 468–496.
- Chiocchetti S., Peshkov I., Gavrilyuk S., Dumbser M. High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension // J. Comput. Phys., 2021, vol. 426, pp. 109898.
- Chiocchetti S., Dumbser M. An exactly curl-free staggered semi-implicit finite volume scheme for a first order hyperbolic model of viscous two-phase flows with surface tension // J. Sci. Comput., 2022, vol. 94, pp. 24.
- Godunov S.K., Romenskii E.I. Elements of Continuum Mechanics and Conservation Laws. Springer US, 2003.
- Peshkov I., Pavelka M., Romenski E., Grmela M. Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations // Contin. Mech.&Thermodyn., 2018, vol. 30, no. 6, pp. 1343–1378.
- Romenski E., Belozerov A.A., Peshkov I.M. Conservative formulation for compressible multiphase flows // Quart. Appl. Math., 2016, vol. 74, pp. 113–136.
- Romenski E., Reshetova G., Peshkov I. Two-phase hyperbolic model for porous media saturated with a viscous fluid and its application to wavefields simulation // Appl. Math. Model., 2022, vol. 106, pp. 567–600.
- Romenski E., Drikakis D., Toro E. Conservative models and numerical methods for compressible two-phase flow // J. Sci. Comput., 2010, vol. 42, no. 1, pp. 68–95.
- Romenski E., Resnyansky A.D., Toro E.F. Conservative hyperbolic formulation for compressible two-phase flow with different phase pressures and temperatures // Quart. Appl. Math., 2007, vol. 65, no. 2, pp. 259–279.
- Godunov S.K., Mikhailova T.Y., Romenskii E.I. Systems of thermodynamically coordinated laws of conservation invariant under rotations // Sib. Math. J., 1996, vol. 37, no. 4, pp. 690–705.
- Godunov S.K., Romenskii E.I. Elements of Mechanics of Continuous Media and Conservation Laws. Novosibirsk: Nauch. Kniga, 1998. 280 p. (in Russian)
- Friedrichs K.O. Symmetric positive linear differential equations // Commun. on Pure&Appl. Math., 1958, vol. 11. no. 3, pp. 333–418.
- Dafermos K.M. Hyperbolic Conservation Laws in Continuum Physics. Berlin: Springer, 2016.
- Dhaouadi F., Dumbser M. A first order hyperbolic reformulation of the Navier–Stokes–Korteweg system based on the GPR model and an augmented Lagrangian approach // J. Comput. Phys., 2022, vol. 470, pp. 111544.
- Dhaouadi F., Gavrilyuk S., Vila J.-P. Hyperbolic relaxation models for thin films down an inclined plane // Appl. Math.&Comput., 2022, vol. 433, pp. 127378.
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