A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing

Journal of Computational Physics

Volumn 183, Issue 1, 2002, Pages 26-82

  Miller, G H ^a,b   Colella, P ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

Adaptive mesh refinement; AMR; Elasticity; Fluid dynamics; Godunov method; Plasticity; Shock waves; Solid mechanics; Solid fluid coupling

Indexed keywords

ELASTOPLASTICITY; FLUID DYNAMICS; MESH GENERATION; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; VOLUME FRACTION;

ADAPTIVE MESH REFINEMENT; AMR; EULERIAN; FLUID-DYNAMICS; GODUNOV METHOD; RIEMANN PROBLEM; SHOCK-CAPTURING; SHOCK-WAVES; SOLID MECHANICS; SOLID-FLUID COUPLING;

SHOCK WAVES;

EID: 0037146399     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2002.7158     Document Type: Article

References (47)

1. T. J. Ahrens, Mineral Physics and Crystallography: A Handbook of Physical Constants (American Geophysical Union, Washington, DC, 1995).
2. D. L. Anderson, Theory of the Earth (Blackwell, Boston, 1989).
3. J. Bell, M. Berger, J. Saltzman, and M. Welcome, Three-dimensional adaptive mesh refinement for hyperbolic conservation laws, SIAM J. Sci. Comput. 15, 127 (1994).
4. J. B. Bell, P. Colella, and M. L. Welcome, Conservative front-tracking for inviscid compressible flow, In AIAA 10th Computational Fluid Dynamics Conference, Honolulu, Hawaii, 1991 (AIAA Press, Washington, DC, 1991), p. 814.
5. J. B. Bell, C. N. Dawson, and G. R. Shubin, An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions, J. Comput. Phys. 74, 1 (1988).
6. M. J. Berger and P. Colella, Local adaptive mesh refinement for shock hydrodynamics, J. Comput. PhYs. 82, 64 (1989).
7. M. J. Berger and I. Rigoutsos, An algorithm for point clustering and grid generation, IEEE Trans. Systems, Man Cybernet. 21, 1278 (1991).
8. H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed. (Wiley, New York, 1985).
9. I.-L. Chern and P. Colella, A Conservative Front Tracking Method for Hyperbolic Conservation Laws, Technical Report UCRL-97200 (Lawrence Livermore National Laboratory, July 1987).
10. P. Colella, Multidimensional upwind methods for hyperbolic conservation laws, J. Comput. Phys. 87, 171 (1990).
11. P. Colella, Volume-of-fluid methods for partial differential equations, in Godunov Methods: Theory and Applications, edited by E. F. Toro (Kluwer, New York, 2001), p. 161.
12. P. Colella and H. M. Glaz, Efficient solution algorithms for the Riemann problem for real gases, J. Comput. Phys. 59, 264 (1985).
13. P. Colella, H. M. Glaz, and R. E. Ferguson, Multifluid Algorithms for Eulerian Finite Difference Methods (1996).
14. P. Colella, D. T. Graves, D. Modiano, D. B. Serafini, and B. van Straalen, Chombo Software Package for AMR Applications, Technical Report (Lawrence Berkeley National Laboratory, 2000), http://seesar.lbl.gov/anag/chombo/.
15. P. Colella and L. F. Henderson, The von Neumann paradox for the diffraction of weak shock waves, J. Fluid. Mech. 213, 71 (1990).
16. P. Colella and P. R. Woodward, The piecewise parabolic method (PPM) for gas dynamical simulations, J. Comput. Phys. 54, 174 (1984).
17. W. Y. Crutchfield and M. Welcome, Object-oriented implementation of adaptive mesh refinement algorithms, Sci. Program. 2(4), 145 (1993).
18. W. Fickett and L. M. Scherr, Numerical Calculation of the Cylinder Test, Technical Report LA-5906 (Los Alamos National Laboratory, 1975).
19. J. Hilditch and P. Colella, A front tracking method for compressible flames in one dimension, SIAM J. Sci. Comput. 16, 755 (1995).
20. C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39, 201 (1981).
21. H. Johansen and P. Colella, A Cartesian grid embedded boundary method for Poisson's equation on irregular domains, J. Comput. Phys. 147, 60 (1998).
22. D. B. Kothe, W. J. Rider, S. J. Mosso, J. S. Brock, and J. I. Hochstein, Volume Tracking of Interfaces Having Surface Tension in Two and Three Dimensions, AIAA 34th Science Meeting, Reno, Nevada, 1996, Paper 96-0859 (1996).
23. E. H. Lee and D. T. Liu, Finite-strain elastic-plastic theory with application to plane-wave analysis, J. Appl. Phys. 38, 19 (1967).
24. A. J. Majda and A. Bourlioux, Theoretical and numerical structure of unstable detonations, Philos. Trans. R. Soc. London 350, (1995).
25. G. H. Miller and P. Colella, A high-order Eulerian Godunov method for elastic-plastic flow in solids, J. Comput. Phys. 167, 131 (2001).
26. G. H. Miller and E. G. Puckett, A high-order Godunov method for multiple condensed phases, J. Comput. Phys. 128, 134 (1996).
27. D. Modiano and P. Colella, A Higher-Order Embedded Boundary Method for Time-Dependent Simulation of Hyperbolic Conservation Laws, Technical Report, LBNL-45239 (Lawrence Berkeley National Laboratory, 2000).
28. M. Mooney, A theory of large elastic deformation, J. Appl. Phys. 11, 582 (1940).
29. W. F. Noh, CEL: A time-dependent, two-space-dimensional, coupled Eulerian-Lagrange code, Methods Comput. Phys. 3, 117 (1964).
30. W. F. Noh and P. R. Woodward, SLIC (Simple Line Interface Calculation), Springer Lecture Notes in Physics (Springer-Verlag, Berlin, 1976), Vol. 59.
31. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1985).
32. R. B. Pember, J. B. Bell, P. Colella, W. Y. Crutchfield, and M. L. Welcome, An adaptive Cartesian grid method for unsteady compressible flow in irregular regions, J. Comput. Phys. 120, 278 (1995).
33. J. E. Pilliod, A Second-Order Unsplit Methodfor Modeling Flames in Two-Dimensional Compressible Flow, PhD thesis (University of California, Davis, 1996).
34. J. E. Pilliod and E. G. Puckett, An unsplit, second-order accurate Godunov method for tracking deflagrations and detonations, in Proceedings of the 21st International Symposium on Shock Waves, edited by Allan Paul Great Keppel Island, Queensland, Australia, July 20-25, 1997, (Pauther, Fyshwick, Australia, 1997), p. 1053.
35. J. E. Pilliod and G. E. Puckett, Second-Order Accurate Volume-of-Fluid Algorithms for Tracking Material Interfaces, Technical Report LBNL-40745 (Lawrence Berkeley National Laboratory, 1997).
36. B. J. Plohr and D. H. Sharp, A conservative formulation for plasticity, Adv. Appl. Math. 13, 462 (1992).
37. E. G. Puckett and J. S. Saltzman, A 3D adaptive mesh refinement algorithm for multimaterial gas dynamics, Physica D 60, 84 (1992).
38. R. S. Rivlin, Large elastic deformations of isotropic materials. IV. further developments of the general theory, Proc. R. Soc. London Ser. A 241, 379 (1948).
39. J. H. Rose, J. Ferrante, and J. R. Smith, Universal binding energy curves for metals and bimetallic interfaces, Phys. Rev. Lett. 47, 675 (1981).
40. J. Saltzman, An unsplit 3D upwind method for hyperbolic conservation laws, J. Comput. Phys. 115, 153 (1994).
41. J. C. Simo and T. J. R. Hughes, Computational Inelasticity (Springer-Verlag, New York, 1997).
42. J. A. Trangenstein and P. Colella, A higher-order Godunov method for modeling finite deformation in elasticplastic solids, Commun. Pure Appl. Math. 44, 41 (1991).
43. B. van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, J. Comput. Phys. 32, 101 (1979).
44. P. Vinet, J. Ferrante, J. H. Rose, and J. R. Smith, Compressibility of solids, J. Geophys. Res. B 92, 9319 (1987).
45. P. Vinet, J. Ferrante, J. R. Smith, and J. H. Rose, A universal equation of state for solids, J. Phys. C 19, L467 (1986).
46. M. L. Wilkins, Calculation of elastic-plastic flow, in Methods in Computational Physics, edited by B. Alder, S. Fernbach, and M. Rotenberg (Academic Press, New York, 1964), Vol. 3, p. 211.
47. P. R. Woodward, Piecewise parabolic methods for astrophysical fluid dynamics, in Astrophysical Radiation Hydrodynamics, edited by K.-H. Winkler and M. Norman (Reidel, Dordrecht, 1986), p. 245.