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Numerical aspects of the smoothed particle hydrodynamics method for simulating accretion disks. (English) Zbl 0923.76202
Summary: The derivation of the smoothed particle hydrodynamics (SPH) method is reviewed. In particular, the problem of second-order derivative terms is investigated. Applying these considerations to the Navier-Stokes equations, a physical viscosity is constructed which can be used to perform simulations of viscous fluids within the framework of SPH. With such a viscous stress tensor, the energy balance and the angular momentum conservation for the particle and the continuum representations are compared. An SPH code based on these results is tested on different problems, especially on an analytically solvable problem, namely the spreading of a ring of gas moving with Keplerian speed around a point mass. Additionally, some examples for the dynamics of accretion disks in close binary systems are presented. Finally, the efficient implementation of this SPH code is discussed in some detail, in particular by a comparison between scalar and vector computers.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
85-08 Computational methods for problems pertaining to astronomy and astrophysics
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[1] Benz, W., ()
[2] Dormand, J.R.; Prince, P.J., J. comput. app. math., 6, 19, (1980)
[3] Flebbe, O.; Münzel, S.; Herold, H.; Riffert, H.; Ruder, H., Astrophys. J., (1994), in press
[4] Frank, J.; King, A.R.; Raine, D.J., Accretion power in astrophysics, (1992), Cambridge University Press
[5] Gingold, R.A.; Monaghan, J.J., Mon. not. roy. astron. soc., 181, 375, (1977)
[6] Harlow, F.H., Meth. comput. phys., 3, 319, (1964)
[7] Hernquist, L.; Katz, N., Astrophys. J. suppl. ser., 70, 419, (1989)
[8] Laguna, P., Preprint PSU-ASTRO 94/2-1, Astrophys. J., (1994), submitted to
[9] Lucy, L.B., Astronom. J., 82, 1013, (1977)
[10] Landau, L.D.; Lifschitz, E.M., Hydrodynamik, (1991), Akademie-Verlag Berlin · Zbl 0997.76501
[11] Lubow, S.H., Astrophys. J., 381, 259, (1991)
[12] Lubow, S.H., Astrophys. J., 381, 268, (1991)
[13] Lubow, S.H., Astrophys. J., 401, 317, (1992)
[14] Martin, T.J.; Pearce, F.R.; Thomas, P.A., Preprint SUSSEX-AST-MPT-1, (1993), Sussex University
[15] Monaghan, J.J., Comput. phys. rep., 3, 71, (1985)
[16] Monaghan, J.J., Ann. rev. astron. astrophys., 30, 543, (1992)
[17] Monaghan, J.J.; Gingold, R.A., J. comput. phys., 52, 374, (1983)
[18] Paczyński, B., Astrophys. J., 216, 822, (1977)
[19] Pringle, J.E., Ann. rev. astron. astrophys., 19, 137, (1981)
[20] Sedgewick, Algorithmen, (1992), Addison-Wesley Reading, MA · Zbl 0838.68042
[21] Whitehurst, R., Mon. not. roy. astron. soc., 232, 35, (1988)
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