Moving-Least-Squares-particle hydrodynamics - I. Consistency and stability

International Journal for Numerical Methods in Engineering

Volumn 44, Issue 8, 1999, Pages 1115-1155

  Dilts, Gary A ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Meshless methods; MLS, Lagrangian hydrodynamics; Moving least squares; Smooth particle hydrodynamics; SPH

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; GALERKIN METHODS; HYDRODYNAMICS; INTERPOLATION;

MOVING LEAST SQUARES PARTICLE HYDRODYNAMICS (MLSPH);

LEAST SQUARES APPROXIMATIONS;

FINITE ELEMENT METHOD; FLUID DYNAMICS; HYDRODYNAMICS; LAGRANGIAN ANALYSIS;

FINITE ELEMENT METHOD; FLUID DYNAMICS; HYDRODYNAMICS; LAGRANGIAN ANALYSIS;

EID: 0033586394     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990320)44:8<1115::AID-NME547>3.0.CO;2-L     Document Type: Article

References (33)

1. R. A. Gingold and J. J. Monaghan, 'Smoothed particle hydrodynamics, theory and application to non-spherical stars', Mon. Not. Roy. Astr. Soc., 181, 375-389 (1977).
2. P. W. Randles, T. C. Carney and L. D. Libersky, 'Continuum dynamical simulations of bomb fragmentation', Proc. 15th Int. Symp. Ballistics, 21-24 May 1995, Jerusalem, Israel, 1995.
3. J. W. Bolstad and L. A. Schwalbe, 'SPHINX hydrocode simulations of low-velocity impact damage on a standard chemical submunition', Los Alamos National Laboratory Document LA-UR 95-3354, 1995.
4. R. F. Stellingwerf and C. A. Wingate, 'Impact modeling with smooth particle hydrodynamics', Los Alamos National Laboratory Document LA-UR-92-1981, 1992.
5. R. F. Stellingwerf and C. A. Wingate, 'SPH calculations of armor penetration by projectiles with combined obliquity and yaw', Los Alamos National Laboratory Document LA-UR-93-4186, 1993.
6. C. A. Wingate, R. F. Stellingwerf, R. F. Davidson and M. W. Burkett, 'Models of high velocity impact phenomena', 'Los Alamos National Laboratory Document LA-UR-92-1982, 1992.
7. D. A. Mandell and C. A. Wingate, 'Prediction of material strength and fracture of glass using the SPHINX smooth particle hydrodynamics code', Los Alamos National Laboratory Report LA-12830, 1994.
8. D. A. Mandell, C. A. Wingate, G. A. Dilts and L. A. Schwalbe, 'Computational brittle fracture using smooth particle hydrodynamics', Los Alamos National Laboratory Report LA-CP-96-209, 1996.
9. R. Gutfraind and S. B. Savage, 'Marginal ice-zone rheology: comparison of results from continuum-plastic models and discrete-particle simulations', J. Geophys. Res. Oceans, 102, 12647-12661 (1997).
10. D. A. Fulk, 'A numerical analysis of smoothed particle hydrodynamics', Thesis, Air Force Institute of Technology, 1994.
11. L. D. Libersky, A. G. Petschek, T. C. Carney, J. R. Hipp and F. A. Allahdadi, 'High strain Lagrangian hydrodynamics', J. Commit. Phys., 109, 67-75 (1993).
12. G. A. Dilts, 'Equivalence of the SPH method and a space-time Galerkin moving particle method', Los Alamos National Laboratory Document LA-UR 96-134, 1996.
13. J. W. Swegle, D. L. Hicks and S. W. Attaway, 'Smoothed particle hydrodynamics stability analysis', J. Comput. Phys., 116, 123-134 (1995).
14. P. W. Randles and L. D. Libersky, 'Smoothed particle hydrodynamics: some recent improvements and applications', Comput. Meth. Appl. Mech. Engng., 139, 375-408 (1996).
15. W. K. Liu, S. Jun and Y. F. Zhang, 'Reproducing kernel particle methods', Int. J. Numer. Meth. Engng., 20, 1081-1106 (1995).
16. C. A. Wingate, R. F. Stellingwerf, 'Los alamos SPHINX manual', Los Alamos National Laboratory Document LA-UR 93-2476, 1993.
17. A. H. Vermeulen, R. H. Bartels and G. R. Heppler, 'Integrating products of B-splines', SIAM J. Sci. Statist. Comput., 13, 1025-1038 (1992).
18. T. Belytschko, Y. Krongauz, D. Organ, M. Fleming and P. Krysl, 'Meshless methods: an overview and recent developments', Comput. Meth. Appl. Mech. Engng., 139, 3-47 (1996).
19. P. Lancaster and K. Salkauskas, 'Surfaces generated by moving least squares methods', Math. Comput., 37, 141-158, (1981).
20. B. Nayroles, G. Touzot and P. Villon, 'Generalizing the finite element method: diffuse approzimation and diffuse elements', Comput Mech., 10, 307-318 (1992).
21. T. Belytschko, Y. Y. Lu and L. Gu, 'Element-free Galerkin methods', Int. J. Numer. Meth. Engng., 37, 229-256 (1994).
22. D. Shepard, 'A two-dimensional interpolation function for irregularly spaced points', Proc. 1968 A.C.M. Nat. Conf., pp. 517-524.
23. C. A. Duarte and J. T. Oden, 'An H-P adaptive method using clouds', Comput. Meth. Appl. Mech. Engng., 139, 237-262 (1996).
24. T. Belytschko, Y. Krongauz, M. Fleming, D. Organ and W. K. Liu, 'Smoothing and accelerated computations in the element-free galerkin method', J. Comput. Appl. Math., 74, 111-126 (1996).
25. M. Shashkov, Conservative Finite-Difference Methods on General Grids, CRC Press, New York, 1996, p. 47.
26. E. Caramana, private remark.
27. D. E. Burton, 'Multidimensional discretization of conservation laws for unstructured polyhedral grids', Lawrence Livermore National Laboratory preprint UCRL-JC-118306, 22 August 1994.
28. E. J. Caramana, D. E. Burton, M. J. Shashkov and P. P. Whalen, 'The construction of compatible hydrodynamics algorithms utilizing conservation of total energy', J. Comput. Phys., to appear.
29. G. R. Johnson and S. R. Beissel, 'Normalized smoothing functions for SPH impact computations', Int. J. Numer. Meth. Engng., 39, 2725-2741 (1996).
30. J. J. Monaghan and R. A. Gingold, 'Shock simulation by the particle method SPH', J. Comput. Phys., 52, 374-389 (1983).
31. W. Benz, private remark.
32. S. Wolfram, Mathematica: A System For Doing Mathematics By Computer, Addison-Wesley, Redwood City, CA, 1991.
33. C. E. Morris, ed., Los Alamos Shock Wave Profile Data, University of California Press, London, 1982, ISBN 0-520-04013-9, p. 79.