Skip to main content
Log in

Anisotropic Closure Model in Mixed Cells

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

The paper offers a new anisotropic closure model for equations of Lagrangian gas dynamics and elastoplastic in mixed cells containing several components (materials). The model is realized in the EGAK code; and numerical investigations of a method on test problems are conducted. The paper presents full statements of two one-dimensional problems and one two-dimensional problem, as well as a description of the processing technique for the results. The numerical results are compared with the results obtained by another closure model available in the EGAK code and with the analytical solutions. The analysis and discussion of the computational results are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Tipton, “CALE mixed zone pressure relaxation,” private commun. (Lawrence Livermore Natl. Laboratory, 1989).

    Google Scholar 

  2. D. Miller and G. Zimmerman, “An algorithm for time evolving volume fractions in mixed zones in lagrangian hydrodynamics calculations,” Report UCRL-PRES-223908 (Lawrence Livermore Natl. Laboratory, 2006).

    Google Scholar 

  3. M. Baer and J. Nunziato, “A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials,” Int. J. Multiphase Flow 12, 861–889 (1986).

    Article  MATH  Google Scholar 

  4. A. Murrone and H. Guillard, “A five equation reduced model for compressible two phase flow problems,” J. Comput. Phys. 202, 664–698 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Kamm, M. Shashkov, J. Fung, A. Harrison, and T. Canfield, “A comparative study of various pressure relaxation closure models for one-dimensional two-material lagrangian hydrodynamics,” Int. J. Numer. Meth. Fluids 65, 1311–1324 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Shashkov, “Closure models for multimaterial cells in arbitrary lagrangian-eulerian hydrocodes,” Int. J. Numer. Meth. Fluids 56, 1497–1504 (2007).

    Article  MATH  Google Scholar 

  7. M. Francois, M. Shashkov, E. Dendy, and R. Lowrie, “Mixture models for multimaterial eulerian and lagrangian hydrocodes,” Report LAUR-10-03391 (Los Alamos Natl. Laboratory, 2010).

    Google Scholar 

  8. Y. Yanilkin, E. Goncharov, V. Kolobyanin, V. Sadchikov, J. Kamm, M. Shashkov, and W. Rider, “Multi-material pressure relaxation methods for lagrangian hydrodynamics,” Comput. Fluids 83, 137–143 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  9. Y. Bondarenko and Y. Yanilkin, “Computation of the thermodynamic parameters in the mixed cells in gas dynamics,” Math. Model. 14, 63–81 (2002).

    MATH  Google Scholar 

  10. V. I. Delov and V. V. Sadchikov, “Comparison of some models for calculation of thermodynamic parameters of lagrange cells with inhomogeneous composition,” Vopr. At. Nauki Tekh., Ser.: Mat. Model. Fiz. Protsessov, No. 1, 57–70 (2005).

    Google Scholar 

  11. E. A. Goncharov and Yu. V. Yanilkin, “The new computational method for thermodynamic state of materials in mixed cells,” Vopr. At. Nauki Tekh., Ser.: Mat. Model. Fiz. Protsessov, No. 3, 16–30 (2004).

    Google Scholar 

  12. A. Barlow, “A new lagrangian scheme for multimaterial cells,” in Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Computational Fluid Dynamics Conference, Swansea–Wales, UK, 2001, pp. 235–294.

    Google Scholar 

  13. A. Despres and F. Lagoutiere, “Numerical solution of two-component compressible fluid model with interfaces,” Prog. Comput. Fluid Dyn. 7, 295–310 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  14. R. Hill, A. Barlow, and M. Shashkov, “Interface-aware sub-scale dynamics closure model,” Report LAUR-12-21959 (Loughborough, UK, 2012).

    Google Scholar 

  15. J. W. Grove, “Pressure-velocity equilibrium hydrodynamic models,” Acta Math. Sci. B 30, 563–594 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  16. S. M. Bakhrakh, V. P. Spiridonov, and A. A. Shanin, “A method for heterogeneous medium gas-dynamic flow computations in lagrangian-eulerian coordinates,” Dokl. Akad. Nauk SSSR 276 (4) (1984).

    Google Scholar 

  17. F. H. Harlow, “The particle-in-cell method for numerical solution of problems in fluid dynamics,” Proc. Symp. Appl. Math. 15, 269(1963).

    Article  Google Scholar 

  18. E. A. Goncharov, V. Yu. Kolobyanin, and Yu. V. Yanilkin, “Closure method of lagrangian gas dynamics in mixed cells based on the equality of component velocities,” Vopr. At. Nauki Tekh., Ser.: Mat. Model. Fiz. Protsessov, No. 4, 100–105 (2006).

    Google Scholar 

  19. A. Barlow, R. Hill, and M. Shashkov, “Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in lagrangian and arbitrary lagrangian-eulerian hydrodynamics,” J. Comput. Phys. 276, 92–135 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  20. Yu. V. Yanilkin, S. P. Belyaev, Yu. A. Bondarenko, et al., “Eulerian numerical methods EGAK and TREK for simulation of multidimensional flows of multicomponent media,” Tr. RFIATS-VNIIEF, No. 12, 54–65 (2008).

    Google Scholar 

  21. E. A. Goncharov, Yu. V. Yanilkin, and V. Yu. Kolobyanin, “On the determination of artificial viscosity for mixed cell compoonents,” Vopr. At. Nauki Tekh., Ser.: Mat. Model. Fiz. Protsessov, No. 2, 15–29 (2010).

    Google Scholar 

  22. Yu. Yanilkin et al., “Study and implementation of multi-material pressure relaxation methods for lagrangian hydrodynamics,” Report under Task Order 039, LANS/VNIIEF Agreement No. 37713-000-02-35, Deliverable 5.2 (LANS, 2010).

  23. Yu. Yanilkin et al., “Study and implementation of multi-material pressure relaxation methods for lagrangian hydrodynamics,” Report under Task Order 039, LANS/VNIIEF Agreement No. 37713-000-02-35, Deliverable 5.3 (LANS, 2011).

  24. Mathematical Simulation of Turbulent Mixing in Compressible Media, Course of Lectures, Ed. by Yu. V. Yanilkin, V. P. Statsenko, and V. I. Kozlov (FGUP RFIATS-VNIIEF, Sarov, 2009) [in Russian].

    Google Scholar 

  25. EGIDA-2D Code for 2D Problems Simulation, The School-Book, Ed. by Yu. V. Yanilkin (FGUP RFIATSVNIIEF, Sarov, 2008), Vol. 1 [in Russian].

  26. A. A. Kraiukhin, V. A. Svidinskii, A. L. Stadnik, and Yu. V. Yanilkin, “Nonstationary problems for testing elastoplasticity codes,” Vopr. At. Nauki Tekh., Ser.: Mat. Model. Fiz. Protsessov, No. 2, 17–30 (2016).

    Google Scholar 

  27. R. Saurel and R. Abgrall, “A multiphase Godunov method for compressible multifluid and multiphase flows,” J. Comput. Phys. 150, 425–467 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  28. B. Plohr, “Shockless acceleration of thin plates modeled by a tracled random choice method,” AIAA J. 26, 470–478 (1988).

    Article  MATH  Google Scholar 

  29. G. Sod, “A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws,” J. Comput. Phys. 27, 1–31 (1978).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Y. V. Yanilkin.

Additional information

Original Russian Text © Y.V. Yanilkin, O.O. Toporova, V.Yu. Kolobyanin, 2017, published in Matematicheskoe Modelirovanie, 2017, Vol. 29, No. 8, pp. 44–58.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yanilkin, Y.V., Toporova, O.O. & Kolobyanin, V.Y. Anisotropic Closure Model in Mixed Cells. Math Models Comput Simul 10, 164–175 (2018). https://doi.org/10.1134/S207004821802014X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S207004821802014X

Keywords

Navigation