Formulations of Artificial Viscosity for Multi-dimensional Shock Wave Computations

Journal of Computational Physics

Volumn 144, Issue 1, 1998, Pages 70-97

  Caramana, E J ^a   Shashkov, M J ^a   Whalen, P P ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; KINETIC ENERGY; KINETICS; NUMERICAL METHODS; VISCOSITY;

ARTIFICIAL VISCOSITY; CONDITION; FUNCTIONAL FORMS; GALILEAN INVARIANT; INTERNAL ENERGIES; MULTI-DIMENSIONAL SHOCK; PROPERTY; SHOCK-WAVES; TURN OFFS; VISCOUS FORCES;

SHOCK WAVES;

EID: 0001840838     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.5989     Document Type: Article

References (28)

1. VonNeumann J., Richtmyer R. D. A method for the numerical calculation of hydrodynamic shocks. J. Appl. Phys. 21:1950;232.
2. E. J. Caramana, D. E. Burton, M. J. Shashkov, P. P. Whalen, The development of compatible hydrodynamics algorithms utilizing conservation of total energy, J. Comput. Phys.
3. Schulz W. D. Two-dimensional Lagrangian hydrodynamic difference schemes. Methods Comput. Phys. 3:1964;1.
4. Christiansen R. B. Godunov Methods on a Staggered Mesh - An Improved Artificial Viscosity. 1991.
5. Benson D. J., Schoenfeld S. A total variation diminishing shock viscosity. Comput. Mech. 11:1993;107.
6. Landshoff R. A Numerical Method for Treating Fluid Flow in the Presence of Shocks. 1955.
7. Wilkins M. L. Use of artificial viscosity in multidimensional shock wave problems. J. Comput. Phys. 36:1980;281.
8. A. P. Favorskii, L. V. Moiseenko, V. F. Tishkin, N. N. Tyurina, The introduction of artificial dissipators into finite-difference schemes of hydrodynamics, M. V. Keldysh Institute of Applied Mathematics, Moscow, Russia, 1982.
9. Mikhailova N. V., Tishkin V. F., Turina N. N., Favorskii A. P., Shashkov M. Yu. Numerical modelling of two-dimensional gas-dynamic flows on a variable structure mesh. USSR Comput. Math. and Math. Phys. 26:1986;74.
10. Richtmyer R. D., Morton K. W. Difference Methods for Initial-Value Problems. 1967;313.
11. van Leer B. Towards the ultimate conservative difference scheme 5: A second order sequel to Godunov's method. J. Comput. Phys. 32:1979;101.
12. Dukowicz J. K. A general, non-iterative Reimann solver for Godunov's method. J. Comput. Phys. 61:1985;119.
13. Kuropatenko V. F. Difference Methods for Solutions of Problems of Mathematical Physics, 1. 1967;116.
14. Mihalas D., Mihalas B. Foundations of Radiation Hydrodynamics. 1984;283.
15. Landau L. D., Lifshitz E. M. Course of theoretical physics. Fluid Mechanics. 6:1982;48.
16. Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49:1983;357.
17. Burton D. E. Exact conservation of energy and momentum in staggered-grid hydrodynamics with arbitrary connectivity. Advances in the Free Lagrange Method. 1990.
18. W. D. Schulz, 1979.
19. 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. 142:1998;521.
20. Burton D. E. Multidimensional Discretization of Conservation Laws for Unstructured Polyhedral Grids. 1994.
21. D. E. Burton.
22. Caramana E. J., Whalen P. P. Numerical preservation of symmetry properties of continuum problems. J. Comput. Phys. 141:1998;174.
23. Margolin L. G. A Centered Artificial Viscosity for Cells with Large Aspect Ratio. 1988.
24. Noh W. F. Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux. J. Comput. Phys. 72:1987;78.
25. Coggeshall S. V., Meyer-ter-Vehn J. Group invariant solutions and optimal systems for multidimensional hydrodynamics. J. Math. Phys. 33:1992;3585.
26. Sedov L. I. Similarity and Dimensional Methods in Mechanics. 1959.
27. Cameron I. G. An analysis of the errors caused by using artificial viscosity terms to represent steady-state flow. J. Comput. Phys. 1:1966;1.
28. Margolin L. G., Ruppel H. M., Demuth R. B. Gradient Scaling for Nonuniform Meshes. 1985.