Artificial Viscosity Methods forModelling Shock Wave Propagation

Chapter

Abstract

The paper gives an overview of the artificial viscoity method widely used today to alow the simulation of problems containg shock waves. The development of the most common basic form of the viscosity term is summarised and its behaviour is illustrated through simulations of a 1D piston problem. Test problems that are commonly used to test different viscosity formulations are then discussed to further illustrate the method. Finally other shock viscosity forms such as edge and tensor viscosities are briefly discussed.

Keywords

Advection 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Von Neumann J., Richtmyer R.D. (1950) A method for the calculation of hydrodynamic shocks. J. Appl. Phys. 21, 232-237.MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Godunov S. K. (1959) A difference scheme for numerical computation of discontinuous solutions of equations in fluid dynamics. Mat. Sb. 47, 271-306.MathSciNetGoogle Scholar
  3. 3.
    Toro E.F. (1999) Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag Berlin HeidelbergGoogle Scholar
  4. 4.
    Wilkins M.L. (1980) Use of artificial viscosity in multidimensional fluid dynamic calculations. J. Comput. Phys. 36, 281-303.MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Landshoff R. (1955) A numerical method for treating fluid flow in the presence of shocks. LA-1930, Los Alamos National Laboratory.Google Scholar
  6. 6.
    Lin J.I. (2004) DYNA3D: A nonlinear, explicit, three-dimensional finite element code for solid and structural mechanics. UCRL-MA-107254, Lawrence Livermore National Laboratory. 19 Artificial Viscosity Methods 365Google Scholar
  7. 7.
    Noh W.F. (1987) Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux. J. Comput. Phys. 72, 78-120.MATHCrossRefGoogle Scholar
  8. 8.
    Rider W.J. (2000) Revisiting wall heating. J. Comput. Phys. 162, 395-410.MATHCrossRefGoogle Scholar
  9. 9.
    Sod G.A. (1978) A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27, 1-31.MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Caramana E.J., Shashkov M.J., Whalen P.P. (1998) Formulations of artificial viscosity for multi-dimensional shock wave computations. J. Comput. Phys. 144, 70-97.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Margolin L.G. (1988) A centered artificial viscosity for cells with large aspect ratios. UCRL-53882, Lawrence Livermore National Laboratory.Google Scholar
  12. 12.
    Benson D.J. (1991) A new two-dimensional flux-limited shock viscosity for impact calculations. Comput. Methods Appl. Mech. Engrg. 93, 39-95.MATHCrossRefGoogle Scholar
  13. 13.
    Benson D.J., Schoenfeld S. (1993) A total variation diminishing shock viscosity. Comput. Mech. 11, 107-121.MATHMathSciNetGoogle Scholar
  14. 14.
    Campbell J.C., Shashkov M.J. (2001) A tensor viscosity using a mimetic finite difference algorithm. J. Comput. Phys. 172, 739-765.MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Kurapatenko V.F. (1967) In: Difference methods for solutions of problems of mathematical physics, I (Editor: N.N. Janenko). Amer. Math. Soc., Providence, R.I., p. 116.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Engineering - AppliedMechanicsCranfield UniversityCranfieldUK

Personalised recommendations