Conservative smoothing stabilizes discrete-numerical instabilities in SPH material dynamics computations

Applied Mathematics and Computation

Volumn 85, Issue 2-3, 1997, Pages 209-226

  Hicks, D L ^a   Swegle, J W ^b   Attaway, S W ^b  

^a MICHIGAN TECHNOLOGICAL UNIVERSITY   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000530706     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(96)00136-1     Document Type: Article

References (27)

1. P. M. Campbell, Some new algorithms for boundary value problems in smooth particle hydrodynamics, Mission Research Corp. Tech. Rep., DNA-TR-88-286, 1988.
2. R. Courant, K. Friedrichs, and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann., 100:32-74 (1928).
3. C. Guenther, D. L. Hicks, and J. W. Swegle, Conservative Smoothing versus artificial viscosity, SNLA SAND94-1853, 1994.
4. I. M. Gel'fand and G. E. Shilov, Generalized Functions, Vol. 1, Academic Press, 1964.
5. R. A. Gingold and J. J. Monaghan, Smoothed particle hydrodynamics: theory and applications to nonspherical stars, Mon. Not. Astr. Soc., 181:375-389 (1977).
6. J. S. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Yale U. Press, 1923.
7. F. Harlow, The Particle-In-Cell (PIC) Method for Numerical Solutions of Problems of Fluid Mechanics, Proc. Symp. in Appl. Math., V15, 269, AMS.
8. W. Herrmann, A Lagrangean finite difference method for two-dimensional motion including material strength, AFWL-TR-64-107, 1964.
9. D. L. Hicks, The Convergence of Numerical Solutions of Hydrodynamic Shock Problems, AFWL-TR-69-20, CHFS AD849487, 1969.
10. D. L. Hicks, Stability Analysis of WONDY (a Hydrocode based on the Artificial Viscosity Method of von Neumann and Richtmyer) for a Special Case of Maxwell's Material Law, Math. Comp., 32(144):1123-1130 (1978).
11. D. L. Hicks and K. L. Kuttler, Error bounds for numerical solutions of hydrodynamical problems including shocks, SIAM J. Num. Analy., 28(3):662-684 (1991).
12. D. L. Hicks, L. M. Liebrock, and Y. Wen, Eigenform error estimates for computational material dynamics with shocks, Part 1.1 Hooke's law materials, Appl. Math. & Comp., 66(2 & 3):181-216 (1994).
13. D. L. Hicks, J. W. Swegle, and S. W. Attaway, SPH: Instabilities, Wall Heating, and Conservative Smoothing, Proc. Workshop on Advances in SPH, C. Wingate and W. Miller, eds., 21-23 Sept. 1993, Los Alamos National Lab., Los Alamos, NM, Los Alamos Rep. LA-UR-93-4375, 223-256.
14. H. Kolsky, A method for the numerical solution of transient hydrodynamic shock problems in two space dimensions, Los Alamos Rep., LA-1867, 1955.
15. R. Landshoff, A numerical method for treating fluid flow in the presence of shocks, Los Alamos. Rep., LA-1930, 1955.
16. P. D. Lax and R. D. Richtmyer, Survey of the stability of linear finite difference equation, Comm. Pure Appl. Math., 9:267 (1956).
17. L. B. Lucy, A numerical approach to the testing of the fission hypothesis, Astr. J. 82:1013-1024 (1977).
18. J. Monaghan and R. Gingold, Shock simulation by the particle method SPH, J. Comp. Physics. 52:374-389 (1983).
19. J. von Neumann and R. Richtmyer, A method for the numerical calculation of hydrodynamic shocks, J. Appl. Physics, 21:232-237 (1950).
20. V. H. Ransom and D. L. Hicks, Hyperbolic two-pressure models for two-phase flow, J. Comp. Physics, 53(1):124-151 (1984).
21. R. Richtmyer and K. Morton, Difference Methods for Initial Value Problems, Interscience Publishers, 1967.
22. J. W. Swegle, S. W. Attaway, M. W. Heinstein, F. J. Mello, and D. L. Hicks, An Analysis of Smoothed Particle Hydrodynamics SNLA SAND93-2513, 1993.
23. J. W. Swegle and D. L. Hicks, Stability and consistency of the SPH Method, Proc. Workshop on Advances in SPH, eds. C. Wingate & W. Miller, 21-23 Sept. 1993, Los Alamos National Lab., Los Alamos, NM, Los Alamos Rep. LA-UR-93-4375, p. 189-222.
24. J. W. Swegle, D. L. Hicks, and S. W. Attaway, Stability Analysis of SPH, J. Comp. Physics, 116:123-134 (1995).
25. Y. Wen, D. L. Hicks, and J. W. Swegle, Stabilizing SPH with Conservative Smoothing, SNLA Report SAND94-1932, 1994.
26. W. Whitaker, E. Nawrocki, C. Needham, and W. Troutman, Theoretical Calculations of the phenomenology of HE detonations, AFWL-TR-66-141, 1966.
27. M. Wilkins, Calculation of elastic-plastic flow, Lawrence Livermore Rep., UCRL-7322, 1963.