Abstract
A technology for building parallel applications for numerical simulation based on hyperbolic partial differential equations is described. A formalization of problems and methods that makes it possible to describe new problems and methods for their solution by configuring the universal technology for specific cases is proposed. Results of numerical simulation of spatial flows in shear layers of a compressible inviscid perfect medium and of the Rayleigh–Taylor instability are presented.
Similar content being viewed by others
References
https://parallel.ru/tech/engineering/pacet2.html
https://ru.wikipedia.org/wiki/Computer-aided_engineering
O. M. Belotserkovskii, A. M. Oparin, and V. M. Chechetkin, Turbulence: New Approaches (Nauka, Moscow, 2002) [in Russian].
T. E. Faber, Fluid Dynamics for physicists (Cambridge Univ. Press, Cambridge, 1995; Гидроаэродинамика. М.: Постмаркет, 2001.
P. R. Spalart, “Strategies for turbulence modeling and simulations,” Int. J. Heat Fluid Flow 21, 252–263 (2000).
A. V. Garbaruk, M. Kh. Strelets, and M. L. Shur, The Capabilities and Limitations of Modern Approaches to the Simulation of Turbulence in Aerodynamics Computations, Textbook (St. Peterburg. Gos. Politekh. Univ., St. Petersburg, 2012) [in Russian].
A. S. Kholodov, Numerical Methods for Hyperbolic Equations and Systems of Equations: A Survey (Mosc. Fiz.-Tekh. Inst., Moscow, 2000) [in Russiam].
L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959; Gostekhteorizdat, 1953).
L. G. Loitsyanskii, Mechanics of Liquids and Gases (Nauka, Moscow, 1978; Begell House, New York, 1995).
Fortova S.V., L. M. Kraginskii, A. V. Chikitkin, and E. I. Oparina, “Software package for solving hyperbolic type equations,” Math. Models Comput. Simul. 5, 607–619 (2013).
V. M. Kovenya, and N. N. Yanenko, The Splitting Method in Fluid Dynamics (Nauka, Novosibirsk, 1981) [in Russian].
P. L. Roe, “Approximate Riemann solvers, parameter vectors and difference scheme,” J. Comput. Phys. 43, 357–372 (1981).
K. M. Magometov and A. S. Kholodov, Grid-Characteristic Numerical Methods (Nauka, Moscow, 1987) [in Russian].
P. L. Roe, “Characteristic-based schemes for the Euler equations,” Ann. Rev. Fluid Mech. 18, 337–365 (1986).
A. Harten, “High resolution schemes for hyperbolic conservation laws,” J. Comput. Phys. 49, 357–393 (1983).
J.Y. Yang, “Third-order nonoscillatory schemes for the Euler equations,” AIAA J. 29 1611–1618 (1991).
B. van Leer, “Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method,” J. Comput. Phys. 32, 101–136 (1979).
A. M. Oparin, “Numerical simulation of problems related to the intensive development of hydrodynamic instabilities,” in Novelties inNumerical Simulation: Algorithms, Computational Experiments, and Results (Nauka, Moscow, 2000), pp. 63–90 [in Russian].
O. M. Belotserkovskii and Yu. M. Davydov, The Method of Large Particles in Fluid Dynamics (Nauka, Moscow, 1982) [in Russian].
K. Fletcher, Computational Techniques for Fluid Dynamics (Springer, New-York, 1991; Mir, Moscow, 1991).
G. Booch, Object-Oriented Design: With Applications (Benjamin, Redwood, 1991; Konkord, Moscow, 1992).
O. M. Belotserkovskii and S. V. Fortova, “Investigation of the cascade mechanism of turbulence development in free shear flow,” Dokl. Phys. 57, 110–113 (2012).
S. V. Fortova, “Investigation of spectrum characteristics of the vortex cascades in shear flow,” Phys. Scripta 155, 014049–014051 (2013).
S. V. Fortova, “Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer,” Comput. Math. Math. Phys. 53, 311–319 (2013).
S. V. Fortova, “Eddy cascade of instabilities and transition to turbulence,” Comput. Math. Math. Phys. 54, 553–561 (2014).
O. M. Belotserkovskii, V. A. Gushchin, and V. N. Kon’shin, “A splitting method for the investigation of flows in the stratified free surface fluid,” Zh. Vych. Mat. Mat. Fiz. 27 (4), 594–609 (1987).
G. Comte-Bellot, Écoulement turbulent entre deux parois parallèles (Service de documentation scientifique et technique de l’armement, Paris, 1965; Mir, Moscow, 1968).
A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk SSSR 30, 453–466 (1941).
A. M. Obukhov, “On the distribution of energy in the turbulence stream spectrum,” Izv. Akad. Nauk SSSR, Ser. Geogr. Gefiz. 5 (4), 453–466 (1941).
V. I. Arnol’d and L. D. Meshalkin, “Kolmogorov’s seminar on selected topics of calculus (1958–1959),” Usp. Mat. Nauk 15 (1), 247–250 (1960).
O. M. Belotserkovskii and A. M. Oparin, Numerical Experiment in Turbulence: From Order to Chaos, 2nd ed. (Nauka, Moscow, 2000) [in Russian].
O. M. Belotserkovskii, Yu. M. Davydov, and A. Yu. Dem’yanov, “The interaction of perturbation modes under the Rayleigh–Taylor instability,” Dokl. Akad. Nauk SSSR 288, 1071 (1986).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.S. Belotserkovskaya, A.P. Pronina, S.V. Fortova, V.V. Shepelev, 2016, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2016, Vol. 56, No. 6, pp. 1185–1196.
To the memory of O.M. Belotserkovskii
Rights and permissions
About this article
Cite this article
Belotserkovskaya, M.S., Pronina, A.P., Fortova, S.V. et al. Application of the program package TURBO problem solver for some fluid dynamics problems. Comput. Math. and Math. Phys. 56, 1162–1173 (2016). https://doi.org/10.1134/S0965542516060075
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542516060075