Advertisement

AMR applied to non-linear Elastodynamics

  • S. A. E. G. Falle
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 41)

Summary

We describe an AMR scheme for non-linear elastodynamics in Lagrangean coordinates. The scheme uses a linear Riemann solver and computes the deformation gradient from the displacements in order to ensure that it is consistent. Solid bodies with stress free boundaries are modeled by embedding them in a very weak material with a smooth transition in material properties at the boundary. A full approximation multigrid is used to compute states in dynamical equilibrium.

Keywords

Sound Speed Deformation Gradient Riemann Problem Adaptive Grid Mesh Spacing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. AF91.
    Arthur, S.J., Falle, S.A.E.G.: Multigrid methods applied to an explosion at a plane density interface. MNRAS, 251, 93–104 (1991)Google Scholar
  2. BBSW94.
    Bell, J., Berger, M., Saltzmann, J., Welcome, M.: Three dimensional dadative mesh refinement for hyperbolic conservation laws. Siam J. Sci. Comput., 15, 127–138 (1994)MathSciNetCrossRefGoogle Scholar
  3. BO84.
    Berger, M.J., Oliger J.:Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys., 53, 484–512 (1984)MathSciNetCrossRefGoogle Scholar
  4. BC89.
    Berger, M.J., Colella, P.: Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys., 82, 64–84 (1989)CrossRefGoogle Scholar
  5. BR82.
    Brandt, A.: Guide to multigrid development. Lect. Notes Math., 960, 220–312 (1982)Google Scholar
  6. FA91.
    Falle, S.A.E.G.: Self-similar jets. MNRAS, 250, 581–596 (1991)Google Scholar
  7. LA73.
    Lax, P.D.: Hyperbolic systems and the mathematical theory of shock waves. Regional conference Series in Applied Mathematics: 11, Philadelphia, Society for Industrial and Applied Mathematics (1973)Google Scholar
  8. MC01.
    Miller, G.H., Colella, P.: A high order Eulerian Godunov method for elastic-plastic flow in solids. J. Comput. Phys., 167, 131–176 (2001)CrossRefGoogle Scholar
  9. OG84.
    Ogden, R.W.: Non-linear elastic deformations. Ellis Horwood (1984)Google Scholar
  10. QU96.
    Quirk, J.J.: A parallel adative grid algorithm for computational shock hydrodynamics. Appl. Numer. Math., 20, 427–453 (1996)zbMATHMathSciNetCrossRefGoogle Scholar
  11. RO86.
    Roe, P.L.: Characteristic-based schemes for the Euler equations. Ann. Rev. Fluid Mech., 18, 337–365 (1986)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • S. A. E. G. Falle
    • 1
  1. 1.Department of Applied MathematicsUniversity of LeedsLeedsUK

Personalised recommendations