A hybrid scheme for gas-dust systems stiffly coupled via viscous drag

Journal of Computational Physics

Volumn 229, Issue 10, 2010, Pages 3916-3937

  Miniati, Francesco ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Godunov methods; Particle in cell methods; Stiff equations

Indexed keywords

DRAG; GASES; INTERFACE STATES; PHASE INTERFACES;

A-STABLE; DUST SYSTEMS; FIRST ORDER; FLUID DESCRIPTION; GODUNOV METHOD; HYBRID SCHEME; PARTICLE IN CELL METHOD; SECOND ORDERS; STIFF EQUATIONS; VISCOUS DRAG;

DUST;

EID: 78449231856     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.01.034     Document Type: Article

References (29)

1. D.S. Balsara, D.A. Tilley, T. Rettig, S.D. Brittain, Dust settling in magnetorotationally driven turbulent discs - I. Numerical methods and evidence for a vigorous streaming instability, Mon. Not. R. Astron. Soc. 397 (2009) 24-43.
2. J.A. Barranco, Three-dimensional simulations of Kelvin-Helmholtz instability in settled dust layers in protoplanetary disks, Astrophys. J. 691 (2009) 907-921.
3. L. Barrière-Fouchet, J.-F. Gonzalez, J.R. Murray, R.J. Humble, S.T. Maddison, Dust distribution in protoplanetary disks. Vertical settling and radial migration, Astr. Astrophys. 443 (2005) 185-194.
4. J.B. Bell, P. Colella, J.A. Trangestein, Higher order Godunov methods for general systems of hyperbolic conservation laws, J. Comput. Phys. 82 (1989) 362-397.
5. J. Birn, J.F. Drake, M.A. Shay, B.N. Rogers, R.E. Denton, M. Hesse, M. Kuznetsova, Z.W. Ma, A. Bhattacharjee, A. Otto, P.L. Pritchett, Geospace environmental modeling (GEM) magnetic reconnection challenge, J. Geoph. Res. 106 (2001) 3715-3720.
6. G.Q. Chen, C. Levermore, T. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Commun. Pure Appl. Math. 47 (1994) 787-830.
7. P. Colella, Multidimensional upwind methods for hyperbolic conservation laws, J. Comput. Phys. 82 (1989) 64-84.
8. J.N. Cuzzi, A.R. Dobrovolskis, J.M. Champney, Particle-gas dynamics in the midplane of a protoplanetary nebula, Icarus 106 (1993). 102+.
9. A. Dutt, L. Greengard, V. Rokhlin, Spectral deferred correction methods for ordinary differential equations, BIT 40 (2000) 241-266.
10. G.B. Field, Thermal instability, Astrophys. J. 142 (1965) 531.
11. S. Fromang, R.P. Nelson, Global MHD simulations of stratified and turbulent protoplanetary discs. II. Dust settling, Astr. Astrophys. 496 (2009) 597-608.
12. E.T. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, second ed., Springer, Berlin, 1997.
13. P. Garaud, L. Barrière-Fouchet, D.N.C. Lin, Individual and average behavior of particles in a protoplanetary nebula, Astrophys. J. 603 (2004) 292-306.
14. A. Johansen, H. Klahr, T. Henning, Gravoturbulent formation of planetesimals, Astrophys. J. 636 (2006) 1121-1134.
15. A. Johansen, J.S. Oishi, M.-M.M. Low, H. Klahr, T. Henning, A. Youdin, Rapid planetesimal formation in turbulent circumstellar disks, Nature 448 (2007) 1022-1025.
16. G. Laibe, J.-F. Gonzalez, L. Fouchet, S.T. Maddison, SPH simulations of grain growth in protoplanetary disks, Astr. Astrophys. 487 (2008) 265-270.
17. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Course of Theoretical Physics, second ed., vol. 6, Pergamon Press, Oxford, 1987.
18. F. Miniati, P. Colella, Block structured adaptive mesh and time refinement for hybrid, hyperbolic + n-body systems, J. Comput. Phys. 227 (2007) 400- 430.
19. F. Miniati, P. Colella, A modified Godunov's scheme for stiff source conservative hydrodynamics, J. Comput. Phys. 224 (2007) 519-538.
20. J.J. Monaghan, A. Kocharyan, SPH simulation of multi-phase flow, Comput. Phys. Commun. 87 (1995) 225-235.
21. D.R. Mott, E.S. Oran, B. van Leer, A quasi-steady-state solver for the stiff ordinary differential equations of reaction kinetics, J. Comput. Phys. 164 (2000) 407-428.
22. Y. Nakagawa, M. Sekiya, C. Hayashi, Settling and growth of dust particles in a laminar phase of a low-mass solar nebula, Icarus 67 (1986) 375-390.
23. E.S. Oran, J.P. Boris, Numerical Simulation of Reactive Flow, second ed., Cambridge University Press, Cambridge, UK, 2000.
24. W.K.M. Rice, G. Lodato, J.E. Pringle, P.J. Armitage, I.A. Bonnell, Accelerated planetesimal growth in self-gravitating protoplanetary discs, Mon. Not. R. Astron. Soc. 355 (2004) 543-552.
25. J. Saltzman, An unsplit 3D upwind method for hyperbolic conservation laws, J. Comput. Phys. 115 (1994) 153-168.
26. D. Trebotich, G.H. Miller, P. Colella, D.T. Graves, D.F. Martin, P.O. Schwartz, A tightly coupled particle-fluid model for dna-laden flows in complex microscale geometries, in: K.J. Bathe (Ed.), Proceedings of the Third MIT Conference on Computational Fluid and Solid Mechanics, MIT, USA, 2005, pp. 1018-1022.
27. G.B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, New York, 1974.
28. A. Youdin, A. Johansen, Protoplanetary disk turbulence driven by the streaming instability: linear evolution and numerical methods, Astrophys. J. 662 (2007) 613-626.
29. A.N. Youdin, J. Goodman, Streaming instabilities in protoplanetary disks, Astrophys. J. 620 (2005) 459-469.