Abstract
The main aspects of the numerical methods used to explore the hydrodynamics of supercritical fluids are discussed. The numerical solution of a system of partial differential equations like the Navier–Stokes equations first requires us to discretize the equations (i.e., replace the continuous variables with discrete ones). The initial system of equations is replaced with linear equations that are solved by appropriate methods according to an algorithm of resolution. The treatment of nonlinear terms in the equations and the simultaneity of the solutions of the different equations are addressed in the algorithm of resolution. These two operations are not independent, since a good choice of discretization scheme often leads more simply and quickly to the solution. Its precision depends on the discretization scheme used, while the efficiency of the resolution in terms of computation time depends on both the discretization scheme and the algorithm.
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References
Accary G, Raspo I (2006) 3-d finite volume methods for the prediction of supercritical fluid buoyant flows in a differentially heated cavity. Comput Fluids 35:1316–1331
Accary G, Raspo I, Bontoux P, Zappoli B (2005) Reverse transition to hydrodynamic stability through the Schwarzschild line in a supercritical fluid layer. Phys Rev E 72(3):035301
Amiroudine S (1995) Modelisation Numerique des Phenomenes de Transport de Chaleur et de Masse dans les Fluides Supercritiques. PhD thesis, IRPHE (Institut de Recherche sur le Phenomènes Hors-Equilibre), Marseille
Amiroudine S, Ouazzani J, Carlès P, Zappoli B (1997) Numerical solution of 1-d unsteady near-critical fluid flows using finite volume methods. Eur J Mech B 16(5):665–680
Chorin AJ (1967) A numerical method for solving the incompressible and low speed compressible equations. J Comput Phys 72:277
Issa RI (1982) Solutions of the implicit discretized fluid flow equations by operator splitting (Mech. Eng. Rep. FS/82/15). Technical report, Imperial College, London
Jang DS, Jetii R, Acharya S (1986) Comparison of the piso, simpler, and simplec algorithms for the treatment of pressure velocity coupling in steady flow problems. Numer Heat Transf 10:209
Li Y, Rudman M (1995) Assessment of higher order upwind schemes incorporating FCT for convection-dominated problems. Numer Heat Transf B 27:1
Ouazzani J, Garrabos Y (2013) A novel numerical approach for low mach number application to supercritical fluids. In: Proceedings of ASME 2013 summer heat transfer conference : HT2013, 14-19 July 2013, Minneapolis, Minnesota, USA. edited by the American Society of Mechanical Engineers. New York (N. Y.): ASME, 2013. p HT2013-17732 (19 p)
Patankar SV (1980) Numerical heat transfers and fluid flows. Hemisphere, Washington
Patankar SV, Spalding DP (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int J Heat Mass Transf 15:1787–1806 (Une methode de calcul du transfert de chaleur, de masse et de quantite de mouvement dans les ecoulements paraboliques tridimensionnels.)
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Zappoli, B., Beysens, D., Garrabos, Y. (2015). Numerical Method. In: Heat Transfers and Related Effects in Supercritical Fluids. Fluid Mechanics and Its Applications, vol 108. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9187-8_22
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DOI: https://doi.org/10.1007/978-94-017-9187-8_22
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