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Unidimensional SPH simulations of reactive shock tubes in an astrophysical perspective. (English) Zbl 1195.76327

Summary: Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method widely used for the modelling of a large variety of astrophysical fluid flows in more than one dimension. Simulations of thermonuclear explosions in stars require, besides the hydrodynamic equations, a realistic equation of state, an energy source term, and a set of nuclear kinetic equations to follow the composition changes of the gas during the explosion. The implementation of a realistic stellar equation of state, and the coupling of hydrodynamics and nuclear burning are investigated in the framework of the simple shock tube geometry. We present and discuss the results of a series of SPH simulations of a detonation in the presence of (1) a single exothermic nuclear reaction, and (2) a restricted network of nuclear reactions. Our results are compared to those of identical simulations performed by other authors using a different hydrodynamic method.

MSC:

76M28 Particle methods and lattice-gas methods
76L05 Shock waves and blast waves in fluid mechanics
76V05 Reaction effects in flows
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics

Software:

FLASH; TREESPH
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[1] Arnett W.D. (1969). A possible model of supernovae: detonation of 12C. Astrophys Space Sci. 5: 180–212
[2] Arnett W.D. (1996). Supernovae and Nucleosynthesis. Princeton University Press, Princeton
[3] Bazán G. and Arnett W.D. (1998). Two-dimensional hydrodynamics of pre-core collapse: oxygen shell burning.. Astrophys. J. 496: 316–332
[4] Benz, W.: Smooth particle hydrodynamics: a review. In: Buchler, J.R. (ed.), The Numerical Modelling of Nonlinear Pulsations: Problems and Prospects, p. 269. Kluwer, Dordrecht (1990)
[5] Benz W. (1997). Three-dimensional simulations of core ignition in sub-Chandrasekhar mass models. In: Ruiz-Lapuente, P., Canal, R. and Isern, J. (eds) Thermonuclear Supernovae, pp 457–474. Kluwer, Dordrecht
[6] Boffin H.M.J. and Anzer U. (1994). Numerical studies of wind accretion using SPH. Astron. Astrophys. 284: 1026–1036
[7] Boisseau J.R., Wheeler J.C., Oran E.S. and Khokhlov A. (1996). The multidimensional structure of detonations in Type Ia supernovae. Astrophys. J. Lett. 471: L99–L102
[8] Clayton D.D. (1983). Principles of Stellar Evolution and Nucleosynthesis. University of Chicago Press, Chicago
[9] Colella P. and Woodward P.R. (1984). The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54: 174–201 · Zbl 0531.76082
[10] Courant R. and Friedrichs K.O. (1948). Supersonic Flow and Shock Waves. Interscience Publishers, New York · Zbl 0041.11302
[11] Cox J.P. and Giuli R.T. (1984). Principles of stellar structure. Gordon and Breach, New York
[12] Fickett W. and Davis W.C. (1979). Detonation. University of California Press, Berkeley
[13] Fowler W.A., Caughlan G.R. and Zimmermann B.A. (1975). Thermonuclear reaction rates II.. Annu Rev. Astron. Astrophys. 13: 69–112
[14] Fryxell B., Olson K., Ricker P., Timmes F.X., Zingale M., Lamb D.Q., MacNeice P., Rosner R., Truran J.W. and Tufo H. (2000). FLASH: an adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes. Astrophys. J. Suppl. Ser. 131: 273–334
[15] Fryxell, B.A., Müller, E., Arnett, W.D.: Hydrodynamics and nuclear burning. Technical report MPA 449, Max-Planck Institut für Physik und Astrophysik (1989, unpublished)
[16] Garcia-Senz D. and Bravo E. (1999). Sub-Chandrasekhar mass models for Type Ia supernovae: single and multipoint ignition. In: Miyama, S.M., Tomisaka, K. and Hanawa, T. (eds) Numerical Astrophysics., pp 281–282. Kluwer, Boston
[17] Gehrz R.D., Truran J.W., Williams R.E. and Starrfield S. (1998). Nucleosynthesis in classical novae and its contribution to the interstellar medium. Publ Astron. Soc. Pac. 110: 3–26
[18] Gingold R.A. and Monaghan J.J. (1977). Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181: 375–389 · Zbl 0421.76032
[19] Herant M. and Benz W. (1992). Postexplosion hydrodynamics of SN 1987A. Astrophys. J. 387: 294–308
[20] Hernquist L. and Katz N. (1989). TREESPH–a unification of SPH with the hierarchical tree method. Astrophys. J. Suppl. Ser. 70: 419–446
[21] Hillebrandt, W.: Supernova explosions. In: Miyama, S.M., Tomisaka, K., Hanawa, T. (eds.), Numerical Astrophysics, pp. 265–272. Kluwer, Boston
[22] Hoffman R., Rauscher T., Heger A. and Woosley S. (2002). New results on nucleosynthesis in massive stars; nuclear data needs for nucleosynthesis.. J. Nucl. Sci. Techn. Suppl. 2: 512–517
[23] Höflich P. and Stein J. (2002). On the thermonuclear runaway in type Ia supernovae: How to run away?. Astrophys. J. 568: 779–790
[24] Katz N. (1992). Dissipational galaxy formation. II. Effects of stellar formation. Astron. J. 391: 502–517
[25] Katz N., Weinberg D.H. and Hernquist L. (1996). Cosmological simulations with TreeSPH. Astrophys. J. Suppl. Ser. 105: 19–35
[26] Kerček A., Hillebrandt W. and Truran J.W. (1999). Three-dimensional simulations of classical novae. Astron. Astrophys. 345: 831–840
[27] Landau L.D. and Lifshitz E.M. (1959). Fluid Mechanics. Pergamon Press, Oxford · Zbl 0146.22405
[28] Liu G.R. and Liu M.B. (2003). Smoothed Particle Hydrodynamics: a Meshfree Particle Method. World Scientific, Singapore · Zbl 1046.76001
[29] Liu M.B., Liu G.R. and Lam K.Y. (2002). Investigations into water mitigation using a meshless particle method. Shock Waves 12: 181–195
[30] Liu M.B., Liu G.R., Lam K.Y. and Zong Z. (2003). Meshfree particle simulation of the detonation process for high explosives in shaped charge unlined cavity configurations. Shock Waves 12: 509–520
[31] Lucy L.B. (1977). A numerical approach to the testing of the fission hypothesis. Astron. J. 82: 1013–1024
[32] Monaghan J.J. (1989). On the problem of penetration in particle methods. J. Comput. Phys. 82: 1–15 · Zbl 0665.76124
[33] Monaghan J.J. (1992). Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys. 30: 543–574
[34] Monaghan J.J. and Gingold R.A. (1983). Shock simulation by the particle method SPH. J. Comput. Phys. 52: 374–389 · Zbl 0572.76059
[35] Monaghan J.J. and Lattanzio J.C. (1985). A refined particle method for astrophysical problems. Astron. Astrophys. 149: 135–143 · Zbl 0622.76054
[36] Monaghan J.J. and Lattanzio J.C. (1991). A simulation of the collapse and fragmentation of cooling molecular clouds. Astrophys. J. 375: 177–189
[37] Morris J.P. and Monaghan J.J. (1997). A switch to reduce SPH viscosity. J. Comput. Phys. 136: 41–50 · Zbl 0889.76065
[38] Müller E. (1986). Nuclear reaction networks and stellar evolution codes: the coupling of composition changes and energyrelease in explosive nuclear burning. Astron. Astrophys. 162: 103–108 · Zbl 0593.76078
[39] Randles P.W. and Libersky L.D. (1996). Smoothed Particle Hydrodynamics: some recent improvements and applications. Comput. Methods Appl. Mech. Eng 139: 375–408 · Zbl 0896.73075
[40] Rasio F.A. and Shapiro S.L. (1991). Collisions of giant with compact objects: hydrodynamical calculations. Astrophys. J. 377: 559–580
[41] Reinecke M., Hillebrandt W. and Niemeyer J.C. (2002). Three-dimensional simulations of Type Ia supernovae. Astron. Astrophys. 391: 1167–1172
[42] Segretain L., Chabrier G. and Mochkovitch R. (1997). The fate of merging white dwarfs. Astrophys. J. 481: 355–362
[43] Sod G.A. (1978). A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27: 1–31 · Zbl 0387.76063
[44] Thacker R.J., Tittley E.R., Pearce F.R., Couchman H.M.P. and Thomas P.A. (2000). Smoothed Particle Hydrodynamics in cosmology: a comparative study of implementations. Mon. Not. R. Astron. Soc. 319: 619–648
[45] Thielemann F.-K., Nomoto K. and Yokoi K. (1986). Explosive nucleosynthesis in carbon deflagration models of Type I supernovae. Astron. Astrophys. 158: 17–33
[46] Timmes F.X. (1999). Integration of nuclear reaction networks for stellar hydrodynamics. Astrophys. J. Suppl. Ser. 124: 241–263
[47] Whitworth A.P., Bhattal A.S., Turner J.A. and Watkins S.J. (1995). Estimating density in Smoothed Particle Hydrodynamics. Astron. Astrophys. 301: 929–932
[48] Yukawa H., Boffin H.M.J. and Matsuda T. (1997). Spiral shocks in three-dimensional accretion discs. Mon. Not. R. Astron. Soc. 292: 321–330
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