Application of a hybrid large-particle method for calculating multicomponent gas mixture flows




hybrid large-particle method, multicomponent gas mixtures, test problems


This paper is devoted to a generalization of a hybrid large-particle method for the numerical simulation of multicomponent gas mixture flows in the presence of gas interfaces with various thermodynamic properties. The method belongs to the class of shock-capturing and interface-capturing algorithms. The employed difference scheme is conservative and uniform and possesses the second order approximation in space and time on smooth solutions. The obtained numerical results show the efficiency of the method in a wide range of Mach numbers and ratios of gas dynamic parameters. The error analysis performed near the contact discontinuities on grids of various resolutions confirms the convergence of numerical results to the self-similar solutions.

Author Biography

D.V. Sadin


  1. J. J. Quirk and S. Karni, “On the Dynamics of a Shock-Bubble Interaction,” J. Fluid Mech. 318, 129-163 (1996).
  2. S. Karni, “Multicomponent Flow Calculation by a Consistent Primitive Algorithm,” J. Comput. Phys. 112, 31-43 (1994).
  3. R. Abgrall, “How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: A Quasi Conservative Approach,” J. Comput. Phys. 125 (1), 150-160 (1996).
  4. J. Glimm, X. Li, Y. Liu, et al., “Conservative Front Tracking with Improved Accuracy,” SIAM J. Numer. Anal. 41 (5), 1926-1947 (2003).
  5. H. Terashima and G. Tryggvason, “A Front-Tracking/Ghost-Fluid Method for Fluid Interfaces in Compressible Flows,” J. Comput. Phys. 228 (11), 4012-4037 (2009).
  6. I. E. Ivanov and I. A. Kryukov, “Numerical Modeling of Multicomponent Gas Flows with Strong Discontinuities of Medium Properties,” Mat. Model. 19 (2), 89-100 (2007).
  7. A. Marquina and P. Mulet, “A Flux-Split Algorithm Applied to Conservative Models for Multicomponent Compressible Flows,” J. Comput. Phys. 185 (1), 120-138 (2003).
  8. V. Coralic and T. Colonius, “Finite-Volume WENO Scheme for Viscous Compressible Multicomponent Flows,” J. Comput. Phys. 274, 95-121 (2014).
  9. A. V. Danilin and A. V. Solovjev, “A Modification of the CABARET Scheme for the Computation of Multicomponent Gaseous Flows,” Vychisl. Metody Programm. 16, 18-25 (2015).
  10. D. V. Sadin, “TVD Scheme for Stiff Problems of Wave Dynamics of Heterogeneous Media of Nonhyperbolic Nonconservative Type,” Zh. Vychisl. Mat. Mat. Fiz. 56 (12), 2098-2109 (2016) [Comput. Math. Math. Phys. 56 (12), 2068-2078 (2016)].
  11. D. V. Sadin, “Schemes with Customizable Dissipative Properties as Applied to Gas-Suspensions Flow Simulation,” Mat. Model. 29 (12), 89-104 (2017).
  12. D. V. Sadin, “A Modification of the Large-Particle Method to a Scheme Having the Second Order of Accuracy in Space and Time for Shockwave Flows in a Gas Suspension,” Vestn. Yuzhn. Ural. Gos. Univ. Ser. Mat. Model. Programm. 12 (2), 112-122 (2019).
  13. G. A. Sod, “A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws,” J. Comput. Phys. 27 (1), 1-31 (1978).
  14. J. Wackers and B. Koren, “A Fully Conservative Model for Compressible Two-Fluid Flow,” Int. J. Numer. Meth. Fluids 47 (10-11), 1337-1343 (2005).
  15. E. Johnsen and T. Colonius, “Implementation of WENO Schemes in Compressible Multicomponent Flow Problems,” J. Comput. Phys. 219 (2), 715-732 (2006).
  16. P. Woodward and P. Colella, “The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks,” J. Comput. Phys. 54 (1), 115-173 (1984).
  17. H. Tang and T. Liu, “A Note on the Conservative Schemes for the Euler Equations,” J. Comput. Phys. 218 (2), 451-459 (2006).
  18. T. G. Liu, B. C. Khoo, and K. S. Yeo, “Ghost Fluid Method for Strong Shock Impacting on Material Interface,” J. Comput. Phys. 190 (2), 651-681 (2003).
  19. R. Abgrall and S. Karni, “Computations of Compressible Multifluids,” J. Comput. Phys. 169 (2), 594-623 (2001).
  20. B. Wang, G. Xiang, and X. Y. Hu, “An Incremental-Stencil WENO Reconstruction for Simulation of Compressible Two-Phase Flows,” Int. J. Multiphase Flow 104, 20-31 (2018).
  21. D. V. Sadin and V. A. Davidchuk, “Comparison of a Modified Large-Particle Method with Some High Resolution Schemes. One-Dimensional Test Problems,” Vychisl. Metody Programm. 20, 138-146 (2019).



How to Cite

Садин Д.В. Application of a Hybrid Large-Particle Method for Calculating Multicomponent Gas Mixture Flows // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2020. 20. 489-497. doi 10.26089/NumMet.v20r443



Section 1. Numerical methods and applications