An oscillation free shockcapturing method for compressible van der Waals supercritical fluid flows
Numerical solutions of the Euler equations using real gas equations of state (EOS) often exhibit serious inaccuracies. The focus here is the van der Waals EOS and its variants (often used in supercritical fluid computations). The problems are not related to a lack of convexity of the EOS since the EOS are considered in their domain of convexity at any mesh point and at any time. The difficulties appear as soon as a density discontinuity is present with the rest of the fluid in mechanical equilibrium and typically result in spurious pressure and velocity oscillations. This is reminiscent of wellknown pressure oscillations occurring with ideal gas mixtures when a mass fraction discontinuity is present, which can be interpreted as a discontinuity in the EOS parameters. We are concerned with pressure oscillations that appear just for a single fluid each time a density discontinuity is present. As a result, the combination of density in a nonlinear fashion in the EOS with diffusion by the numerical method results in violation of mechanical equilibrium conditions which are not easy to eliminate, even under grid refinement.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Univ. of Illinois at UrbanaChampaign, Urbana, IL (United States)
 Aix Marseille Univ. and Univ. Institute of France, Marseille Cedex (France); RS2N SAS, Saint Zacharie (France)
 Ecole Centrale Paris, ChatenayMalabry (France); Lab. d'Energetique Moleculaire et Macroscopique, ChatenayMalabry (France)
 Publication Date:
 Grant/Contract Number:
 NA0002382
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 335; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA10)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; shockcapturing methods; real equation of state; Van der Waals; nonconservative equations; pressure oscillations; 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1343123
 Alternate Identifier(s):
 OSTI ID: 1352895; OSTI ID: 1411835
Pantano, C., Saurel, R., and Schmitt, T.. An oscillation free shockcapturing method for compressible van der Waals supercritical fluid flows. United States: N. p.,
Web. doi:10.1016/j.jcp.2017.01.057.
Pantano, C., Saurel, R., & Schmitt, T.. An oscillation free shockcapturing method for compressible van der Waals supercritical fluid flows. United States. doi:10.1016/j.jcp.2017.01.057.
Pantano, C., Saurel, R., and Schmitt, T.. 2017.
"An oscillation free shockcapturing method for compressible van der Waals supercritical fluid flows". United States.
doi:10.1016/j.jcp.2017.01.057. https://www.osti.gov/servlets/purl/1343123.
@article{osti_1343123,
title = {An oscillation free shockcapturing method for compressible van der Waals supercritical fluid flows},
author = {Pantano, C. and Saurel, R. and Schmitt, T.},
abstractNote = {Numerical solutions of the Euler equations using real gas equations of state (EOS) often exhibit serious inaccuracies. The focus here is the van der Waals EOS and its variants (often used in supercritical fluid computations). The problems are not related to a lack of convexity of the EOS since the EOS are considered in their domain of convexity at any mesh point and at any time. The difficulties appear as soon as a density discontinuity is present with the rest of the fluid in mechanical equilibrium and typically result in spurious pressure and velocity oscillations. This is reminiscent of wellknown pressure oscillations occurring with ideal gas mixtures when a mass fraction discontinuity is present, which can be interpreted as a discontinuity in the EOS parameters. We are concerned with pressure oscillations that appear just for a single fluid each time a density discontinuity is present. As a result, the combination of density in a nonlinear fashion in the EOS with diffusion by the numerical method results in violation of mechanical equilibrium conditions which are not easy to eliminate, even under grid refinement.},
doi = {10.1016/j.jcp.2017.01.057},
journal = {Journal of Computational Physics},
number = C,
volume = 335,
place = {United States},
year = {2017},
month = {2}
}