An entropy stable finite volume method for a compressible two phase model

Eduard Feireisl; Mădălina Petcu; Bangwei She

Applications of Mathematics (2023)

  • Volume: 68, Issue: 4, page 467-483
  • ISSN: 0862-7940

Abstract

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We study a binary mixture of compressible viscous fluids modelled by the Navier-Stokes-Allen-Cahn system with isentropic or ideal gas law. We propose a finite volume method for the approximation of the system based on upwinding and artificial diffusion approaches. We prove the entropy stability of the numerical method and present several numerical experiments to support the theory.

How to cite

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Feireisl, Eduard, Petcu, Mădălina, and She, Bangwei. "An entropy stable finite volume method for a compressible two phase model." Applications of Mathematics 68.4 (2023): 467-483. <http://eudml.org/doc/299334>.

@article{Feireisl2023,
abstract = {We study a binary mixture of compressible viscous fluids modelled by the Navier-Stokes-Allen-Cahn system with isentropic or ideal gas law. We propose a finite volume method for the approximation of the system based on upwinding and artificial diffusion approaches. We prove the entropy stability of the numerical method and present several numerical experiments to support the theory.},
author = {Feireisl, Eduard, Petcu, Mădălina, She, Bangwei},
journal = {Applications of Mathematics},
keywords = {compressible Navier-Stokes-Allen-Cahn; finite volume method; entropy stability},
language = {eng},
number = {4},
pages = {467-483},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An entropy stable finite volume method for a compressible two phase model},
url = {http://eudml.org/doc/299334},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Feireisl, Eduard
AU - Petcu, Mădălina
AU - She, Bangwei
TI - An entropy stable finite volume method for a compressible two phase model
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 4
SP - 467
EP - 483
AB - We study a binary mixture of compressible viscous fluids modelled by the Navier-Stokes-Allen-Cahn system with isentropic or ideal gas law. We propose a finite volume method for the approximation of the system based on upwinding and artificial diffusion approaches. We prove the entropy stability of the numerical method and present several numerical experiments to support the theory.
LA - eng
KW - compressible Navier-Stokes-Allen-Cahn; finite volume method; entropy stability
UR - http://eudml.org/doc/299334
ER -

References

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  1. Abels, H., Feireisl, E., 10.1512/iumj.2008.57.3391, Indiana Univ. Math. J. 57 (2008), 659-698. (2008) Zbl1144.35041MR2414331DOI10.1512/iumj.2008.57.3391
  2. Blesgen, T., 10.1088/0022-3727/32/10/307, J. Phys. D, Appl. Phys. 32 (1999), 1119-1123. (1999) DOI10.1088/0022-3727/32/10/307
  3. Ciarlet, P. G., 10.1137/1.9780898719208, Classics in Applied Mathematics 40. SIAM, Philadelphia (2002). (2002) Zbl0999.65129MR1930132DOI10.1137/1.9780898719208
  4. Lukáčová-Medviďová, E. Feireisl M., Mizerová, H., She, B., 10.1051/m2an/2019043, ESAIM, Math. Model. Numer. Anal. 53 (2019), 1957-1979 DOI 10.1051/m2an/2019043 Experiment 2: time evolution of , from top to bottom are . (2019) Zbl1447.35243MR4031688DOI10.1051/m2an/2019043
  5. Feireisl, E., Lukáčová-Medviďová, M., Mizerová, H., She, B., 10.1007/978-3-030-73788-7, MS&A. Modeling, Simulation and Applications 20. Springer, Cham (2021). (2021) Zbl1493.76001MR4390192DOI10.1007/978-3-030-73788-7
  6. Feireisl, E., Lukáčová-Medviďová, M., Mizerová, H., She, B., 10.1093/imanum/draa060, IMA J. Numer. Anal. 41 (2021), 2388-2422. (2021) Zbl07528308MR4328388DOI10.1093/imanum/draa060
  7. Feireisl, E., Petcu, M., Pražák, D., 10.1002/mma.5436, Math. Methods Appl. Sci. 42 (2019), 1465-1479. (2019) Zbl1420.35185MR3928163DOI10.1002/mma.5436
  8. Feireisl, E., Petcu, M., She, B., 10.1007/s10915-021-01624-7, J. Sci. Comput. 89 (2021), Article ID 14, 32 pages. (2021) Zbl1489.35183MR4304552DOI10.1007/s10915-021-01624-7
  9. Feireisl, E., Petzeltová, H., Rocca, E., Schimperna, G., 10.1142/S0218202510004544, Math. Models Methods Appl. Sci. 20 (2010), 1129-1160. (2010) Zbl1200.76155MR2673413DOI10.1142/S0218202510004544
  10. VanderZee, E., Hirani, A. N., Guoy, D., Ramos, E. A., 10.1137/090748214, SIAM J. Sci. Comput. 31 (2010), 4497-4523. (2010) Zbl1253.65030MR2594991DOI10.1137/090748214

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