Computational formulas of the Godunov method are given for the equations of a generalized-equilibrium model of a heterogeneous medium on a curvilinear grid; with the use of this method, the problems of interaction of air shock waves with bubbles of various gases are investigated. Flow of a gas–liquid mixture in a nozzle mouthpiece is considered. The Prandtl–Meyer flow of a water–air mixture is calculated and compared with a self-similar solution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. S. Surov, The Busemann flow for a one-velocity model of a heterogeneous medium, J. Eng. Phys. Thermophys., 80, No. 4, 681–688 (2007).
J. Wackers and B. Koren, A fully conservative model for compressible two-fluid flow, J. Numer. Meth. Fluids, 47, 1337–1343 (2005).
A. Murrone and H. Guillard, A five equation reduced model for compressible two phase flow problems, J. Comput. Phys., 202, 664–698 (2005).
V. Deledicque and M. V. Papalexandris, A conservative approximation to compressible two-phase flow models in the stiff mechanical relaxation limit, J. Comput. Phys., 227, 9241–9270 (2008).
R. Saurel, F. Petitpas, and R. A. Berry, Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures, J. Comput. Phys., 228, 1678–1712 (2009).
J. J. Kreeft and B. Koren, A new formulation of Kapila’s five-equation model for compressible two-fluid flow, and its numerical treatment, J. Comput. Phys., 229, 6220–6242 (2010).
V. S. Surov and I. V. Berezanskii, About the divergent form of equations for a one-velocity multicomponent mixture, J. Eng. Phys. Thermophys., 88, No. 5, 1248–1255 (2015).
S. K. Godunov, A. V. Zabrodin, M. Ya. Ivanov, A. N. Kraiko, and G. P. Prokopov, Numerical Solution of Multidimensional Problems of Gas Dynamics [in Russian], Nauka, Moscow (1976).
V. S. Surov, On equations of a one-velocity heterogeneous medium, J. Eng. Phys. Thermophys., 82, No. 1, 75–84 (2009).
G. B. Wallis, One-Dimensional Two-Phase Flow [Russian translation], Mir, Moscow (1972).
V. S. Surov, Modeling of the interaction of an underwater shock wave and an obstacle in the presence of a bubble screen, J. Eng. Phys. Thermophys., 89, No. 1, 90–99 (2016).
V. S. Surov, Riemann problem for the one-velocity model of a multicomponent liquid, Teplofiz. Vys. Temp., 47, No. 2, 283–291 (2009).
E. F. Toro, Riemann solvers with evolved initial condition, Int. J. Numer. Meth. Fluids, 52, 433–453 (2006).
V. S. Surov, Shock adiabat of a one-velocity heterogeneous medium, J. Eng. Phys. Thermophys., 79, No. 5, 886–892 (2006).
V. S. Surov, Certain self-similar problems of a one-velocity heterogeneous medium, J. Eng. Phys. Thermophys., 80, No. 6, 1237–1246 (2007).
V. S. Surov, On location of contact surfaces in multifluid hydrodynamics, J. Eng. Phys. Thermophys., 83, No. 3, 549–559 (2010).
V. S. Surov, Interaction of shock waves with bubble liquid droplets, Zh. Tekh. Fiz., 71, No. 6, 17–22 (2001).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 89, No. 5, pp. 1237–1240, September–October, 2016.
Rights and permissions
About this article
Cite this article
Surov, V.S. The Godunov Method for Calculating Multidimensional Flows of a One-Velocity Multicomponent Mixture. J Eng Phys Thermophy 89, 1227–1240 (2016). https://doi.org/10.1007/s10891-016-1486-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-016-1486-5