DOI: https://doi.org/10.26089/NumMet.v16r341

A modification of the CABARET scheme for numerical simulation of multicomponent gaseous flows in two-dimensional domains

Authors

  • A.V. Danilin
  • A.V. Solovjev
  • A.M. Zaitsev

Keywords:

one-velocity multicomponent medium
systems of hyperbolic equations
CABARET scheme
computational fluid dynamics (CFD)
conservative methods
finite volume methods
turbulent mixing

Abstract

An explicit numerical algorithm for calculation of two-dimensional motion of multicomponent gas mixtures is proposed. A physical model as well as conservative and characteristic forms of governing equations are given. The discretization of the governing equations is made in accordance with the CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) approach. The proposed algorithm is tested on problems of air shock waves passing through dense and dilute volume inhomogeneities with initial conditions adopted from numerical and experimental studies of other authors. A good agreement between the results of these studies and those obtained by the CABARET approach is shown.

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Published

2015-08-04

Issue

Vol. 16 (2015): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biographies

A.V. Danilin

Nuclear Safety Institute (IBRAE) of RAS
• Junior Researcher

A.V. Solovjev

Nuclear Safety Institute (IBRAE) of RAS
• Leading Researcher

A.M. Zaitsev

Nuclear Safety Institute (IBRAE) of RAS
• Junior Researcher

References

  1. R. Abgrall, “How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: A Quasi Conservative Approach,” J. Comput. Phys. 125 (1), 150-160 (1996).
  2. V. M. Goloviznin and A. A. Samarskii, “Some Characteristics of Finite Difference Scheme ’Cabaret’,” Mat. Model. 10 (1), 101-116 (1998).
  3. V. M. Goloviznin and S. A. Karabasov, “Nonlinear Correction of Cabaret Scheme,” Mat. Model. 10 (12), 107-123 (1998).
  4. V. M. Goloviznin, S. A. Karabasov, and I. M. Kobrinskii, “Balance-Characteristic Schemes with Separated Conservative and Flux Variables,” Mat. Model. 15 (9), 29-48 (2003).
  5. V. M. Goloviznin, “Balanced Characteristic Method for 1D Systems of Hyperbolic Conservation Laws in Eulerian Representation,” Mat. Model. 18 (11), 14-30 (2006).
  6. S. A. Karabasov and V. M. Goloviznin, “Compact Accurately Boundary-Adjusting High-Resolution Technique for Fluid Dynamics,” J. Comput. Phys. 228 (19), 7426-7451 (2009).
  7. V. G. Kondakov, A Generalization of the ’Cabaret’ Scheme to Multidimensional Equations of Gas Dynamics , Candidate’s Dissertation in Mathematics and Physics (Moscow State Univ., Moscow, 2014).
  8. J. J. Quirk and S. Karni, “On the Dynamics of a Shock-Bubble Interaction,” J. Fluid Mech. series 318}, 129-163 (1996).
  9. J. W. Jacobs, “The Dynamics of Shock Accelerated Light and Heavy Gas Cylinders,” Phys. Fluids A series 5} (9), 2239-2247 (1993).
  10. R. S. Lagumbay, Modeling and Simulation of Multiphase/Multicomponent Flows , PhD Thesis (University of Colorado, Boulder, 2006).
  11. K. R. Bates, N. Nikiforakis, and D. Holder, “Richtmyer-Meshkov Instability Induced by the Interaction of a Shock Wave with a Rectangular Block of {@@m SF}_6,” Phys. Fluids 19 (2007).
    doi 10.1063/1.2565486
  12. J.-F. Haas and B. Sturtevant, “Interaction of Weak Shock Waves with Cylindrical and Spherical Gas Inhomogeneities,” J. Fluid Mech. 181, 41-76 (1987).
  13. D. A. Holder, A. V. Smith, C. J. Barton, and D. L. Youngs, “Shock-Tube Experiments on Richtmyer-Meshkov Instability Growth Using an Enlarged Double-Bump Perturbation,” Laser Part. Beams 21 (3), 411-418 (2003).
  14. 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).
  15. M. Latini, O. Schilling, W. S. Don, “Effects of WENO Flux Reconstruction Order and Spatial Resolution on Reshocked Two-Dimensional Richtmyer-Meshkov Instability,” J. Comput. Phys. 221 (2), 805-836 (2007).
  16. R. L. Holmes, J. W. Grove, and D. H. Sharp, “Numerical Investigation of Richtmyer-Meshkov Instability Using Front Tracking,” J. Fluid Mech. 301, 51-64 (1995).
  17. R. H. Cohen, W. P. Dannevik, A. M. Dimits, et al., “Three-Dimensional Simulation of a Richtmyer-Meshkov Instability with a Two-Scale Initial Perturbation,” Phys. Fluids 14, 3692-3709 (2002).
  18. B. D. Collins and J. W. Jacobs, “PLIF Flow Visualization and Measurements of the Richtmyer-Meshkov Instability of an Air/SF6 Interface,” J. Fluid Mech. 464, 113-136 (2002).