Parallel implementation of multiscale approach to the numerical study of gas microflows




gas dynamics, molecular dynamics, parallel algorithms and programs, microchannels, multiscale computations, supercomputing simulation


This paper is devoted to a parallel implementation of multiscale approach to the numerical study of gas flows in microchannels of complex technical systems. The multiscale approach combines the solutions of quasigasdynamic (QGD) equations and molecular dynamics (MD) equations. The proposed parallel implementation of this approach is based on the method of splitting into physical processes and the domain decomposition method. The implementation is oriented for using computer systems with central and hybrid architectures. The developed parallel algorithms show a good scalability. The obtained results confirm the efficiency of the approach under consideration. This approach was used to find the basic coefficient dependences for the QGD system by MD methods and to study a three-dimensional gas flow numerically.

Author Biographies

V.O. Podryga

S.V. Polyakov


  1. A. P. Alkhimov, S. V. Klinkov, V. F. Kosarev, and V. M. Fomin, Cold Gas Dynamic Spraying: Theory and Practice (Fizmatlit, Moscow, 2010; Cambridge Int. Sci. Pub., Cambridge, 2011).
  2. D. Resnick, “Nanoimprint Lithography,” in Nanolithography. The Art of Fabricating Nanoelectronic and Nanophotonic Devices and Systems (Woodhead Publ., Cambridge, 2014), pp. 315-347.
  3. V. O. Podryga, “Molecular Dynamics Method for Simulation of Thermodynamic Equilibrium,” Mat. Model. 22 (11), 39-48 (2010) [Math. Models Comput. Simul. 3 (3), 382-388 (2011)].
  4. V. O. Podryga and S. V. Polyakov, Molecular Dynamic Simulation of Thermodynamic Equilibrium Problem for Heated Nickel , Preprint No. 41 (Keldysh Inst. Appl. Math., Moscow, 2014).
  5. V. O. Podryga and S. V. Polyakov, “Molecular Dynamic Simulation of Thermodynamic Equilibrium Establishment in Nickel,” Mat. Model. 27 (3), 3-19 (2015) [Math. Models Comput. Simul. 7 (5), 456-466 (2015)].
  6. V. O. Podryga, “Determination of Real Gas Macroparameters by Molecular Dynamics,” Mat. Model. 27 (7), 80-90 (2015).
  7. V. O. Podryga, S. V. Polyakov, and D. V. Puzyrkov, “Supercomputer Molecular Modeling of Thermodynamic Equilibrium in Gas-Metal Microsystems,” Vychisl. Metody Programm. 16, 123-138 (2015).
  8. V. O. Podryga, S. V. Polyakov, and V. V. Zhakhovskii, “Atomistic Calculation of the Nitrogen Transitions in Thermodynamic Equilibrium over the Nickel Surface,” Mat. Model. 27 (7), 91-96 (2015).
  9. T. A. Kudryashova and S. V. Polyakov, “A Model of Supersonic Binary Gas Flow,” Mathematica Montisnigri 24, 120-127 (2012).
  10. T. A. Kudryashova, V. O. Podryga, and S. V. Polyakov, “Simulation of Gas Mixture Flows in Microchannels,” Vestn. Peoples’ Friendship Univ. Ser. Mat. Inf. Phys., No. 3, 154-163 (2014).
  11. Yu. N. Karamzin, T. A. Kudryashova, and S. V. Polyakov, “Supercomputer Simulation of Nonlinear Processes in Technical Microsystems,” in Proc. 10th Int. Conf. on Mesh Methods for Boundary-Value Problems and Applications, Kazan, Russia, September 24-29, 2014 (Kazan Federal Univ., Kazan, 2014), pp. 367-374.
  12. Yu. N. Karamzin, T. A. Kudryashova, V. O. Podryga, and S. V. Polyakov, “Multiscale Simulation of Nonlinear Processes in Technical Microsystems,” Mat. Model. 27 (7), 65-74 (2015).
  13. G. Ciccotti and W. G. Hoover (Eds.), Molecular-Dynamics Simulation of Statistical-Mechanical Systems (Elsevier, Amsterdam, 1986).
  14. J. M. Haile, Molecular Dynamics Simulations: Elementary Methods (Wiley, New York, 1992.)
  15. D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Academic, San Diego, 2002).
  16. G. Sutmann, “Classical Molecular Dynamics,” in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, Lecture Notes, NIC Series (John von Neumann Inst. for Computing, Jülich, 2002), Vol. 10, pp. 211-254.
  17. M. P. Allen, “Introduction to Molecular Dynamics Simulation,” in Computational Soft Matter: From Synthetic Polymers to Proteins, Lecture Notes, NIC Series (John von Neumann Inst. for Computing, Jülich, 2004), Vol. 23, pp. 1-28.
  18. G. E. Norman and V. V. Stegailov, “Stochastic Theory of the Classical Molecular Dynamics Method,” Mat. Model. 24 (6), 3-44 (2012) [Math. Models Comput. Simul. 5 (4), 305-333 (2013)].
  19. T. G. Elizarova, Quasi-Gas Dynamic Equations (Springer, Heidelberg, 2009).
  20. V. Garzó, A. Santos, and J. J. Brey, “A Kinetic Model for a Multicomponent Gas,” Phys. Fluids A. 1 (2), 380-383 (1989).
  21. T. G. Elizarova, A. A. Zlotnik, and B. N. Chetverushkin, “On Quasi-Gasdynamic and Quasi-Hydrodynamic Equations for Binary Gas Mixtures,” Dokl. Akad. Nauk 459 (4), 395-399 (2014) [Dokl. Math. 90 (3), 719-723 (2014)].
  22. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, Oxford, 1994).
  23. J. W. Buddenberg and C. R. Wilke, “Calculation of Gas Mixture Viscosities,” Ind. Eng. Chem. 41 (7), 1345-1347 (1949).
  24. C. R. Wilke, “A Viscosity Equation for Gas Mixtures,” J. Chem. Phys. 18 (4), 517-519 (1950).
  25. A. A. Dorofeev, Fundamentals of Theory of Heat Rocket Engines: Theory, Calculation, and Design (Bauman Tech. Univ., Moscow, 2014) [in Russian].
  26. S. Brunauer, Adsorption of Gases and Vapors (Princeton Univ. Press, Princeton, 1945; Inostrannaya Literatura, Moscow, 1948).
  27. G. N. Abramovich, Applied Gas Dynamics (Nauka, Moscow, 1991), Part 1 [in Russian].
  28. G. Mie, “Zur Kinetischen Theorie der Einatomigen Körper,” Ann. Phys. 11 (8), 657-697 (1903).
  29. L. R. Fokin and A. N. Kalashnikov, “The Transport Properties of an N_2-H_2 Mixture of Rarefied Gases in the EPIDIF Database,” Teplofiz. Vys. Temp. 47 (5), 675-687 (2009) [High Temp. 47 (5), 643-655 (2009)].
  30. M. S. Daw and M. I. Baskes, “Embedded-Atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals,” Phys. Rev. B 29 (12), 6443-6453 (1984).
  31. X. W. Zhou, R. A. Johnson, and H. N. G. Wadley, “Misfit-Energy-Increasing Dislocations in Vapor-Deposited CoFe/NiFe Multilayers,” Phys. Rev. B 69 (14), 144113-1-144113-10 (2004).
  32. J. E. Lennard-Jones, “Cohesion,” Proc. Phys. Soc. 43 (5), 461-482 (1931).
  33. H. A. Lorentz, “Über die Anwendung des Satzes vom Virial in der Kinetischen Theorie der Gase,” Ann. Phys. 248, 127-136 (1881).
  34. D. Berthelot, “Sur le Mélange des Gaz,” C. R. Acad. Sci. 126, 1703-1706 (1889).
  35. P. M. Morse, “Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels,” Phys. Rev. 34, 57-64 (1929).
  36. S. Maruyama, “Molecular Dynamics Method for Microscale Heat Transfer,” in Advances in Numerical Heat Transfer (Taylor and Francis, New York, 2000), Vol. 2, pp. 189-226.
  37. D. V. Sivukhin, The General Course of Physics , Vol. 2: Thermodynamics and Molecular Physics (Nauka, Moscow, 1975) [in Russian].
  38. H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, et al., “Molecular Dynamics with Coupling to an External Bath,” J. Chem. Phys. 81, 3684-3690 (1984).
  39. D. W. Heermann, Computer Simulation Methods in Theoretical Physics (Springer, Berlin, 1986; Nauka, Moscow, 1990).
  40. I. V. Fryazinov, “The Balance Method and Variational-Difference Schemes,” Differ. Uravn. 16 (7), 1332-1343 (1980).
  41. A. A. Samarskii, A. V. Koldoba, Yu. A. Poveshchenko, V. F. Tishkin, and A. P. Favorskii, Difference Schemes on Irregular Grids (Kriterii, Minsk, 1996) [in Russian].
  42. R. Eymard, T. R. Gallouet, and R. Herbin, “The Finite Volume Method,” in Handbook of Numerical Analysis (North Holland, Amsterdam, 2000), Vol. 7, pp. 713-1020.
  43. I. V. Popov and I. V. Fryazinov, “Method of Adaptive Artificial Viscosity for the Equations of Gas Dynamics on Triangular and Tetrahedral Grids,” Mat. Model. 24 (6), 109-127 (2012) [Math. Models Comput. Simul. 5 (1), 50-62 (2013)].
  44. L. Verlet, “Computer ’Experiments’ on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules,” Phys. Rev. 159, 98-103 (1967).
  45. A. Toselli and O. B. Widlund, Domain Decomposition Methods - Algorithms and Theory (Springer, Berlin, 2005).
  46. S. V. Polyakov, Yu. N. Karamzin, O. A. Kosolapov, et al., “Hybrid Supercomputer Platform and Application Programming for the Solution of Continuous Mechanics Problems by Grid Methods,” Izv. Southern Federal Univ., Ser. Tekh. Nauki, No. 6, 105-115 (2012).
  47. The Message Passing Interface (MPI) Standard. . Cited April 15, 2016.
  48. The OpenMP API Specification for Parallel Programming. Tutorials. . Cited April 15, 2016.
  49. CUDA Toolkit Documentation. . Cited April 15, 2016.
  50. G. Karypis and V. Kumar, METIS: A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices. . Cited April 15, 2016.
  51. G. Karypis and K. Schloegel, ParMETIS: Parallel Graph Partitioning and Sparse Matrix Ordering Library. . Cited April 15, 2016.



How to Cite

Подрыга В., Поляков С. Parallel Implementation of Multiscale Approach to the Numerical Study of Gas Microflows // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2016. 17. 147-165. doi 10.26089/NumMet.v17r214



Section 1. Numerical methods and applications