An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows

Pantano, C.; Saurel, R.; Schmitt, T.

doi:10.1016/j.jcp.2017.01.057

Title: An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows

Journal Article · Tue Jan 31 23:00:00 EST 2017 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2017.01.057 · OSTI ID:1343123

Pantano, C. ^[1]; Saurel, R. ^[2]; Schmitt, T. ^[3]

Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States); NA-113
Aix Marseille Univ. and Univ. Institute of France, Marseille Cedex (France); RS2N SAS, Saint Zacharie (France)
Ecole Centrale Paris, Chatenay-Malabry (France); Lab. d'Energetique Moleculaire et Macroscopique, Chatenay-Malabry (France)

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 well-known 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.

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Research Organization:: California Inst. of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA-10)

Grant/Contract Number:: NA0002382

OSTI ID:: 1343123

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 335; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (39)

Systems of conservation laws Lax, Peter; Wendroff, Burton Communications on Pure and Applied Mathematics, Vol. 13, Issue 2 https://doi.org/10.1002/cpa.3160130205	journal	May 1960
Multicomponent Flow Calculations by a Consistent Primitive Algorithm Karni, Smadar Journal of Computational Physics, Vol. 112, Issue 1 https://doi.org/10.1006/jcph.1994.1080	journal	May 1994
How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: A Quasi Conservative Approach Abgrall, Rémi Journal of Computational Physics, Vol. 125, Issue 1 https://doi.org/10.1006/jcph.1996.0085	journal	April 1996
An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems Shyue, Keh-Ming Journal of Computational Physics, Vol. 142, Issue 1 https://doi.org/10.1006/jcph.1998.5930	journal	May 1998
A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows Saurel, Richard; Abgrall, Rémi Journal of Computational Physics, Vol. 150, Issue 2 https://doi.org/10.1006/jcph.1999.6187	journal	April 1999
A Fluid-Mixture Type Algorithm for Compressible Multicomponent Flow with van der Waals Equation of State Shyue, Keh-Ming Journal of Computational Physics, Vol. 156, Issue 1 https://doi.org/10.1006/jcph.1999.6349	journal	November 1999
A Fluid-Mixture Type Algorithm for Compressible Multicomponent Flow with Mie–Grüneisen Equation of State Shyue, Keh-Ming Journal of Computational Physics, Vol. 171, Issue 2 https://doi.org/10.1006/jcph.2001.6801	journal	August 2001
Roe Linearization for the van der Waals Gas Guardone, A.; Vigevano, L. Journal of Computational Physics, Vol. 175, Issue 1 https://doi.org/10.1006/jcph.2001.6915	journal	January 2002
A Five-Equation Model for the Simulation of Interfaces between Compressible Fluids Allaire, Grégoire; Clerc, Sébastien; Kokh, Samuel Journal of Computational Physics, Vol. 181, Issue 2 https://doi.org/10.1006/jcph.2002.7143	journal	September 2002
Restoration of the contact surface in the HLL-Riemann solver Toro, E. F.; Spruce, M.; Speares, W. Shock Waves, Vol. 4, Issue 1 https://doi.org/10.1007/BF01414629	journal	July 1994
Thermodynamic analysis and numerical resolution of a turbulent - fully ionized plasma flow model Saurel, R.; Chinnayya, A.; Renaud, F. Shock Waves, Vol. 13, Issue 4 https://doi.org/10.1007/s00193-003-0216-z	journal	December 2003
Approximate Riemann solvers, parameter vectors, and difference schemes Roe, P. L. Journal of Computational Physics, Vol. 43, Issue 2 https://doi.org/10.1016/0021-9991(81)90128-5	journal	October 1981
Uniformly high order accurate essentially non-oscillatory schemes, III Harten, Ami; Engquist, Bjorn; Osher, Stanley Journal of Computational Physics, Vol. 71, Issue 2 https://doi.org/10.1016/0021-9991(87)90031-3	journal	August 1987
Efficient implementation of essentially non-oscillatory shock-capturing schemes Shu, Chi-Wang; Osher, Stanley Journal of Computational Physics, Vol. 77, Issue 2 https://doi.org/10.1016/0021-9991(88)90177-5	journal	August 1988
A weak formulation of roe's approximate riemann solver Toumi, I. Journal of Computational Physics, Vol. 102, Issue 2 https://doi.org/10.1016/0021-9991(92)90378-C	journal	October 1992
Proposition de méthodes et modèles eulériens pour les problèmes à interfaces entre fluides compressibles en présence de transfert de chaleur Massoni, J.; Saurel, R.; Nkonga, B. International Journal of Heat and Mass Transfer, Vol. 45, Issue 6 https://doi.org/10.1016/S0017-9310(01)00238-1	journal	March 2002
Efficient numerical approximation of compressible multi-material flow for unstructured meshes Abgrall, R.; Nkonga, B.; Saurel, R. Computers & Fluids, Vol. 32, Issue 4 https://doi.org/10.1016/S0045-7930(02)00012-9	journal	May 2003
Roe-type schemes for dense gas flow computations Cinnella, P. Computers & Fluids, Vol. 35, Issue 10 https://doi.org/10.1016/j.compfluid.2005.04.007	journal	December 2006
Consistent numerical diffusion terms for simulating compressible multicomponent flows Terashima, Hiroshi; Kawai, Soshi; Koshi, Mitsuo Computers & Fluids, Vol. 88 https://doi.org/10.1016/j.compfluid.2013.10.007	journal	December 2013
A five equation reduced model for compressible two phase flow problems Murrone, Angelo; Guillard, Hervé Journal of Computational Physics, Vol. 202, Issue 2 https://doi.org/10.1016/j.jcp.2004.07.019	journal	January 2005
A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations Saurel, Richard; Franquet, Erwin; Daniel, Eric Journal of Computational Physics, Vol. 223, Issue 2 https://doi.org/10.1016/j.jcp.2006.10.004	journal	May 2007
Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes Castro, Manuel J.; LeFloch, Philippe G.; Muñoz-Ruiz, María Luz Journal of Computational Physics, Vol. 227, Issue 17 https://doi.org/10.1016/j.jcp.2008.05.012	journal	September 2008
Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures Journal of Computational Physics, Vol. 228, Issue 5 https://doi.org/10.1016/j.jcp.2008.11.002	journal	March 2009
A comment on the computation of non-conservative products Abgrall, Rémi; Karni, Smadar Journal of Computational Physics, Vol. 229, Issue 8 https://doi.org/10.1016/j.jcp.2009.12.015	journal	April 2010
An interface capturing method for the simulation of multi-phase compressible flows Shukla, Ratnesh K.; Pantano, Carlos; Freund, Jonathan B. Journal of Computational Physics, Vol. 229, Issue 19 https://doi.org/10.1016/j.jcp.2010.06.025	journal	September 2010
Approach for simulating gas–liquid-like flows under supercritical pressures using a high-order central differencing scheme Terashima, Hiroshi; Koshi, Mitsuo Journal of Computational Physics, Vol. 231, Issue 20 https://doi.org/10.1016/j.jcp.2012.06.021	journal	August 2012
Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state Lee, Bok Jik; Toro, Eleuterio F.; Castro, Cristóbal E. Journal of Computational Physics, Vol. 246 https://doi.org/10.1016/j.jcp.2013.03.046	journal	August 2013
A diffuse interface model with immiscibility preservation Tiwari, Arpit; Freund, Jonathan B.; Pantano, Carlos Journal of Computational Physics, Vol. 252 https://doi.org/10.1016/j.jcp.2013.06.021	journal	November 2013
An Eulerian interface sharpening algorithm for compressible two-phase flow: The algebraic THINC approach Shyue, Keh-Ming; Xiao, Feng Journal of Computational Physics, Vol. 268 https://doi.org/10.1016/j.jcp.2014.03.010	journal	July 2014
A novel numerical flux for the 3D Euler equations with general equation of state Toro, Eleuterio F.; Castro, Cristóbal E.; Lee, Bok Jik Journal of Computational Physics, Vol. 303 https://doi.org/10.1016/j.jcp.2015.09.037	journal	December 2015
Vapor-Liquid Critical Properties of Elements and Compounds. 2. Normal Alkanes Ambrose, Douglas; Tsonopoulos, Constantine Journal of Chemical & Engineering Data, Vol. 40, Issue 3 https://doi.org/10.1021/je00019a001	journal	May 1995
A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems Gallouët, Thierry; Hérard, Jean-Marc; Seguin, Nicolas ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 36, Issue 6 https://doi.org/10.1051/m2an:2003009	journal	November 2002
Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations Kapila, A. K.; Menikoff, R.; Bdzil, J. B. Physics of Fluids, Vol. 13, Issue 10 https://doi.org/10.1063/1.1398042	journal	October 2001
On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws Harten, Amiram; Lax, Peter D.; Leer, Bram van SIAM Review, Vol. 25, Issue 1 https://doi.org/10.1137/1025002	journal	January 1983
Nonclassical Shocks and Kinetic Relations: Strictly Hyperbolic Systems Hayes, Brian T.; LeFloch, Philippe G. SIAM Journal on Mathematical Analysis, Vol. 31, Issue 5 https://doi.org/10.1137/S0036141097319826	journal	January 2000
A Simple Method for Compressible Multifluid Flows Saurel, Richard; Abgrall, Rémi SIAM Journal on Scientific Computing, Vol. 21, Issue 3 https://doi.org/10.1137/S1064827597323749	journal	January 1999
Large-Eddy Simulation of Supercritical-Pressure Round Jets Schmitt, Thomas; Selle, Laurent; Ruiz, Anthony AIAA Journal, Vol. 48, Issue 9 https://doi.org/10.2514/1.J050288	journal	September 2010
High-Resolution Numerical Method for Supercritical Flows with Large Density Variations Terashima, Hiroshi; Kawai, Soshi; Yamanishi, Nobuhiro AIAA Journal, Vol. 49, Issue 12 https://doi.org/10.2514/1.J051079	journal	December 2011
A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws Loubère, Raphaël; Dumbser, Michael; Diot, Steven Communications in Computational Physics, Vol. 16, Issue 3 https://doi.org/10.4208/cicp.181113.140314a	journal	September 2014

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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Van der Waals
nonconservative equations
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real equation of state
shock-capturing methods

Title: An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows

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