Multiscale Simulation for the System of Radiation Hydrodynamics

Abstract

This paper aims at the simulation of multiple scale physics for the system of radiation hydrodynamics. The system couples the fluid dynamic equations with the radiative heat transfer. The coupled system is solved by the gas-kinetic scheme (GKS) for the compressible inviscid Euler flow and the unified gas-kinetic scheme (UGKS) for the non-equilibrium radiative transfer, together with the momentum and energy exchange between these two phases. For the radiative transfer, due to the possible large variation of fluid opacity in different regions, the transport of photons through the flow system is simulated by the multiscale UGKS, which is capable of naturally capturing the transport process from the photon’s free streaming to the diffusive wave propagation. Since both GKS and UGKS are finite volume methods, all unknowns are defined inside each control volume and are discretized consistently in the updates of hydrodynamic and radiative variables. For the coupled system, the scheme has the asymptotic preserving property, such as recovering the equilibrium diffusion limit for the radiation hydrodynamic system in the optically thick region, where the cell size is not limited by photon’s mean free path. A few test cases, such as radiative shock wave problems, are used to validate the current approach.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

References

  1. 1.

    Mihala, D., Mihala, B.W.: Foundations of Radiation Hydrodynamics. Oxford University Press, New York (1984)

    Google Scholar 

  2. 2.

    Lowrie, R.B., Morel, J.E., Hittinger, J.A.: The coupling of radiation and hydrodynamics. Astrophys. J. 521, 432–450 (1999)

    Article  Google Scholar 

  3. 3.

    Lowrie, R.B., Wollaber, A.B.: Simple material-motion corrections for thermal radiactive transport. In: 23rd International Conference on Transport Theory, Santa Fe, NM, USA, 15–20 September 2013

  4. 4.

    McClarren, R.G., Evans, T.M., Lowrie, R.B., Densmore, J.D.: Semi-implicit time integration for Pn thermal radiative transfer. J. Comput. Phys. 227, 7561–7586 (2008)

    MathSciNet  Article  Google Scholar 

  5. 5.

    Lowrie, R.B.: A comparison of implicit time integration methods for nonlinear relaxation and diffusion. J. Comput. Phys. 196, 566–590 (2004)

    Article  Google Scholar 

  6. 6.

    Knoll, D.A., Lowrie, R.B., Morel, J.E.: Numerical analysis of time integration errors for nonequilibrium radiation diffusion. J. Comput. Phys. 226, 1332–1347 (2007)

    Article  Google Scholar 

  7. 7.

    Olson, G.L.: Second-order time evolution of Pn equations for radiation transport. J. Comput. Phys. 228, 3027–3083 (2009)

    Article  Google Scholar 

  8. 8.

    Axelrod, T.S., Dubois, P.F., Rhoades Jr., C.E.: An implicit scheme for calculating time- and fequency-dependent flux limited radiation diffusion in one dimension. J. Comput. Phys. 54, 205–220 (1984)

    Article  Google Scholar 

  9. 9.

    Stone, J.M., Mihalas, D.: Upwind monotonic interpolation methods for the solution of the time dependent radiative transfer equation. J. Comput. Phys. 100, 402–408 (1992)

    Article  Google Scholar 

  10. 10.

    Brown, P.N., Shumaker, D.E., Woodward, C.S.: Fully implicit solution of large-scale non-equilibrium radiation diffusion with high order time integration. J. Comput. Phys. 204, 760–783 (2005)

    MathSciNet  Article  Google Scholar 

  11. 11.

    Sun, W.J., Jiang, S., Xu, K.: An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations. J. Comput. Phys. 285, 265–279 (2015)

    MathSciNet  Article  Google Scholar 

  12. 12.

    Sun, W.J., Jiang, S., Xu, K., Li, S.: An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations. J. Comput. Phys. 302, 222–238 (2015)

    MathSciNet  Article  Google Scholar 

  13. 13.

    Sun, W.J., Jiang, S., Xu, K.: An implicit unified gas kinetic scheme for radiative transfer with equilibrium and non-equilibrium diffusive limits. Commun. Comput. Phys. 22, 899–912 (2017)

    MathSciNet  Article  Google Scholar 

  14. 14.

    Toro, E.: Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer, New York (1999)

    Google Scholar 

  15. 15.

    Xu, K.: A gas-kinetic BGK scheme for the Navier–Stokes equations and its connection with artifical dissipation and Godunov method. J. Comput. Phys. 171, 289–335 (2001)

    MathSciNet  Article  Google Scholar 

  16. 16.

    Kadioglu, S.Y., Knoll, D.A., Lowrie, R.B., Rauenzahn, R.M.: A second order self-consistent IMEX method for radiation hydrodynamics. J. Comput. Phys. 229, 8313–8332 (2010)

    MathSciNet  Article  Google Scholar 

  17. 17.

    Bolding, S., Hansel, J., Edwards, J.D., Morel, J.E., Lowrie, R.B.: Second-order discretization in space and time for radiation-hydrodynamics. J. Comput. Phys. 32, 101–136 (2017)

    MathSciNet  MATH  Google Scholar 

  18. 18.

    Lowrie, R.B., Edwards, J.D.: Radiative shock solutions with grey non-equillibrium diffusion. Shock Waves 18, 129–143 (2008)

    Article  Google Scholar 

  19. 19.

    Dai, W., Woodward, P.R.: Numerical simulations for radiation hydrodynamics. I. Diffusion limit. J. Comput. Phys. 142, 182–207 (1998)

    MathSciNet  Article  Google Scholar 

  20. 20.

    Bates, J.W., Knoll, D.A., Rider, W.J., Lowrie, R.B., Mousseau, V.A.: On consistent time-integration methods for radiation hydrodynamics in the equilibrium diffusion limit: low-energy-density regime. J. Comput. Phys. 167, 99–130 (2001)

    Article  Google Scholar 

  21. 21.

    Sun, W.J., Jiang, S., Xu, K.: A multidimensional unified gas-kinetic scheme for radiative transfer equations on unstructured mesh. J. Comput. Phys. 351, 455–472 (2017)

    MathSciNet  Article  Google Scholar 

  22. 22.

    Xu, K.: Direct Modeling for Computational Fluid Dynamics: Construction and Application of Unified Gas Kinetic Schemes. World Scientific, Singapore (2015)

    Google Scholar 

  23. 23.

    Xu, K.: A gas-kinetic BGK scheme for the Navier–Stokes equations and its connection with artificial dissipation and Godunov method. J. Comput. Phys. 171, 289–335 (2001)

    MathSciNet  Article  Google Scholar 

  24. 24.

    Sekora, M., Stone, J.: A higher order godunov method for radiation hydrodynamics: radiation subsystem. Commun. Appl. Comput. Math. 4, 135–152 (2009)

    MathSciNet  Article  Google Scholar 

  25. 25.

    Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases I: small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525 (1954)

    Article  Google Scholar 

  26. 26.

    van Leer, B.: Towards the ultimate conservative difference schemes V. A second-order sequal to Godunov’s method. J. Comput. Phys. 32, 101–136 (1979)

    Article  Google Scholar 

  27. 27.

    Chandrasekhar, S.: Radiative Transfer. Dover Publications, Mineola (1960)

    Google Scholar 

  28. 28.

    Xu, K., Huang, J.C.: A unified gas-kinetic scheme for continuum and rarefied flows. J. Comput. Phys. 229, 7747–7764 (2010)

    MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

The current research is supported by NSFC (No. 11671048), CAEP foundation (No. CX20200026), National key project (GJXM92579) and Science Challenge Project (No. TZ2016002) for Sun; by NSFC (Grant Nos. 11631008, GZ1465, 11571046) for Jiang; and by Hong Kong research grant council (16206617) and NSFC (Grant Nos. 11772281, 91852114) for Xu.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Kun Xu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sun, W., Jiang, S., Xu, K. et al. Multiscale Simulation for the System of Radiation Hydrodynamics. J Sci Comput 85, 25 (2020). https://doi.org/10.1007/s10915-020-01337-3

Download citation

Keywords

  • Radiation hydrodynamics
  • Asymptotic preserving
  • Gas kinetic scheme
  • Unified gas kinetic scheme
  • Radiative shock wave