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ALE Method for Simulations of Laser-Produced Plasmas

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Finite Volumes for Complex Applications VI Problems & Perspectives

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 4))

Abstract

Simulations of laser-produced plasmas are essential for laser-plasma interaction studies and for inertial confinement fusion (ICF) technology. Dynamics of such plasmas typically involves regions of large scale expansion or compression, which requires to use the moving Lagrangian coordinates. For some kind of flows such as shear or vortex the moving Lagrangian mesh however tangles and such flows require the use of arbitrary Lagrangian Eulerian (ALE) method. We have developed code PALE (Prague ALE) for simulations of laser-produced plasmas which includes Lagrangian and ALE hydrodynamics complemented by heat conductivity and laser absorption. Here we briefly review the numerical methods used in PALE code and present its selected applications to modeling of laser interaction with targets.

MSC2010: 35L65, 35K05, 65M08

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References

  1. Barth, T., Jespersen, D.: The design and application of upwind schemes on unstructured meshes. Tech. Rep. AIAA-89-0366, AIAA, NASA Ames Research Center (1989)

    Google Scholar 

  2. Campbell, J., Shashkov, M.: A tensor artificial viscosity using a mimetic finite difference algorithm. J. Comput. Phys. 172(2), 739–765 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Caramana, E., Shashkov, M.J., Whalen, P.: Formulations of artificial viscosity for multi-dimensional shock wave computations. J. Comput. Phys. 144, 70–97 (1998)

    Article  MathSciNet  Google Scholar 

  4. Caramana, E.J., Burton, D.E., Shashkov, M.J., Whalen, P.P.: The construction of compatible hydrodynamics algorithms utilizing conservation of total energy. J. Comput. Phys. 146(1), 227–262 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Caramana, E.J., Loubère, R.: "curl-q": A vorticity damping artificial viscosity for Lagrangian hydrodynamics calculations. J. Comput. Phys. 215(2), 385–391 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Caramana, E.J., Shashkov, M.J.: Elimination of artificial grid distortion and hourglass-type motions by means of Lagrangian subzonal masses and pressures. J. Comput. Phys. 142, 521–561 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ganzha, V., Liska, R., Shashkov, M., Zenger, C.: Mimetic finite difference methods for diffusion equations on unstructured triangular grid. In: M. Feistauer, V. Dolejší, P. Knobloch, K. Najzar (eds.) Numerical Mathematics and Advanced Applications ENUMATH 2003, pp. 368–377. Springer-Verlag, Berlin (2004)

    Chapter  Google Scholar 

  8. Hirt, C., Amsden, A., Cook, J.: An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14, 227–253 (1974). Reprinted in vol. 135(2), 203–216, 1997.

    Google Scholar 

  9. Kapin, T., Kuchařík, M., Limpouch, J., Liska, R.: Hydrodynamic simulations of laser interactions with low-density foams. Czechoslovak Journal of Physics 56, B493–B499 (2006)

    Article  Google Scholar 

  10. Knupp, P.: Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part I – a framework for surface mesh optimization. Int. J. Numer. Meth. Eng. 48, 401–420 (2000)

    Google Scholar 

  11. Knupp, P., Margolin, L., Shashkov, M.: Reference Jacobian optimization-based rezone strategies for arbitrary Lagrangian Eulerian methods. J. Comput. Phys. 176, 93–128 (2002)

    Article  MATH  Google Scholar 

  12. Kuchařík, M., Limpouch, J., Liska, R.: Laser plasma simulations by arbitrary Lagrangian Eulerian method. J. de Physique IV 133, 167–169 (2006)

    Article  Google Scholar 

  13. Kuchařík, M., Liska, R., Loubere, R., Shashkov, M.: Arbitrary Lagrangian-Eulerian (ALE) method in cylindrical coordinates for laser plasma simulations. In: S. Benzoni-Gavage, D. Serre (eds.) Hyperbolic Problems: Theory, Numerics, Applications, pp. 687–694. Springer (2008)

    Google Scholar 

  14. Kuchařík, M., Shashkov, M., Wendroff, B.: An efficient linearity-and-bound-preserving remapping method. J. Comput. Phys. 188(2), 462–471 (2003)

    Article  MATH  Google Scholar 

  15. Limpouch, J., Liska, R., Kuchařík, M., Váchal, P., Kmetík, V.: Laser-driven collimated plasma flows studied via ALE code. In: 37th EPS Conference on Plasma Physics, pp. P4.222, 1–4. European Physical Society, Mulhouse (2010)

    Google Scholar 

  16. Liska, R., Shashkov, M., Váchal, P., Wendroff, B.: Optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian-Eulerian methods. J. Comput. Phys. 229(5), 1467–1497 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Liska, R., Shashkov, M., Váchal, P., Wendroff, B.: Synchronized flux corrected remapping for ale methods. Computers and Fluids (2011). DOI: 10.1016/j.compfluid.2010.11.013

    MATH  Google Scholar 

  18. Liska, R., Shashkov, M., Wendroff, B.: Lagrangian composite schemes on triangular unstructured grids. In: M. Kočandrlová, V. Kelar (eds.) Mathematical and Computer Modelling in Science and Engineering, pp. 216–220. Prague (2003)

    Google Scholar 

  19. Loubere, R., Ovadia, J., Abgrall, R.: A Lagrangian discontinuous Galerkin type method on unstructured meshes to solve hydrodynamics problems. Int. J. Numer. Meth. Fluids 44(6), 645–663 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Loubère, R., Shashkov, M.: A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. J. Comput. Phys. 209(1), 105–138 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. Loubère, R., Staley, M., Wendroff, B.: The repair paradigm: New algorithms and applications to compressible flow. J. Comput. Phys. 211(2), 385–404 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. Maire, P.H.: A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes. J. Comput. Phys. 228(7), 2391–2425 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Maire, P.H., Abgrall, R., Breil, J., Ovadia, J.: A cell-centered Lagrangian scheme for two-dimensional compressible flow problems. SIAM Journal on Scientific Computing 29(4), 1781–1824 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Renner, O., Liska, R., Rosmej, F.: Laser-produced plasma-wall interaction. Laser and Particle Beams 27(4), 725–731 (2009)

    Article  Google Scholar 

  25. Shashkov, M., Steinberg, S.: Solving diffusion equation with rough coefficients in rough grids. J. Comput. Phys. 129, 383–405 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  26. Shashkov, M., Wendroff, B.: A composite scheme for gas dynamics in Lagrangian coordinates. J. Comput. Phys. 150, 502–517 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  27. Váchal, P., Garimella, R., Shashkov, M.: Untangling of 2D meshes in ALE simulations. J. Comput. Phys. 196(2), 627–644 (2004)

    Article  MATH  Google Scholar 

  28. Winslow, A.: Equipotential zoning of two-dimensional meshes. Tech. Rep. UCRL-7312, Lawrence Livermore National Laboratory (1963)

    Google Scholar 

Download references

Acknowledgements

This research has been supported in part by the Czech Ministry of Education grants MSM6840770022 and LC528, Czech Science Foundation grant GAP205/10/0814 and Czech Technical University grant SGS10/299/OHK4/3T/14.The authors thank M. Shashkov, B. Wendroff, R. Loubere, P.-H. Maire, V. Kmetik, R. Garimella, M. Berndt for fruitful discussions and constructive comments.

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Correspondence to R. Liska .

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Liska, R. et al. (2011). ALE Method for Simulations of Laser-Produced Plasmas. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_87

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