A 3D spectral anelastic hydrodynamic code for shearing, stratified flows

Journal of Computational Physics

Volumn 219, Issue 1, 2006, Pages 21-46

  Barranco, Joseph A ^a   Marcus, Philip S ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Anelastic approximation; Coordinate mapping; Hydrodynamics; Infinite domain; Rotating flows; Shear flows; Spectral methods; Stratified flows; Vortex dynamics

Indexed keywords

AERODYNAMICS; CHEBYSHEV POLYNOMIALS; CODES (SYMBOLS); EULER EQUATIONS; POLYNOMIALS; ROTATING DISKS; SHEAR FLOW; VORTEX FLOW;

ANELASTIC APPROXIMATIONS; COORDINATE MAPPING; HYDRODYNAMIC CODES; INFINITE DOMAINS; PROTOPLANETARY DISKS; ROTATING FLOW; SPECTRAL METHODS; STRATIFIED FLOWS; VERTICAL DIRECTION; VORTEX DYNAMICS;

HYDRODYNAMICS;

EID: 33750379240     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.03.015     Document Type: Article

References (44)

1. Adams F., and Watkins R. Vortices in circumstellar disks. Astrophys. J. 451 (1995) 314-327
2. Balbus S., and Hawley J. A powerful local shear instability in weakly magnetized disks. I. Linear analysis. Astrophys. J. 376 (1991) 214-222
3. Balbus S., and Hawley J. Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys. 70 (1998) 1-53
4. Bannon P. On the anelastic approximation for a compressible atmosphere. J. Atmos. Sci. 53 (1996) 3618-3628
5. Barge P., and Sommeria J. Did planet formation begin inside persistent gaseous vortices?. Astron. Astrophys. 295 (1995) L1-L4
6. J. Barranco, P. Marcus, Vorticies in protoplanetary disks and the formation of planetesimals, in: Center for Turbulence Research - Proceedings of the 2000 Summer Program, 2000, pp. 97-108.
7. Barranco J., and Marcus P. Three-dimensional vortices in stratified protoplanetary disks. Astrophys. J. 623 (2005) 1157-1170
8. J. Barranco, P. Marcus, M. Umurhan, Scalings and asymptotics of coherent vortices in protoplanetary disks, in: Center for Turbulence Research - Proceedings of the 2000 Summer Program, 2000, pp. 85-96.
9. Blaes O., and Balbus S. Local shear instabilities in weakly ionized, weakly magnetized disks. Astrophys. J. 421 (1994) 163-177
10. Boyd J. Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: preserving boundary conditions and interpretation of the filter as a diffusion. J. Comput. Phys. 143 (1998) 283-288
11. Boyd J. Chebyshev and Fourier Spectral Methods (2000), Dover, Mineola, NY
12. Cain A., Ferziger J., and Reynolds W. Discrete orthogonal function expansions for non-uniform grids using the fast Fourier transform. J. Comput. Phys. 56 (1984) 272-286
13. Canuto C., Hussaini M., Quarteroni A., and Zang T. Spectral Methods in Fluid Dynamics (1988), Springer, New York
14. Chandrasekhar S. The stability of non-dissipative Couette flow in hydromagnetics. Proc. Natl. Acad. Sci. USA 46 (1960) 253-257
15. Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability (1961), Dover, New York
16. Cho J., de la Torre Juárez M., Ingersoll A., and Dritschel D. A high-resolution, three-dimensional model of Jupiter's Great Red Spot. J. Geophys. Res. 106 (2001) 5099-5105
17. Dowling T., Fischer A., Gierasch P., Harrington J., Lebeau R., and Santori C. The Explicit Planetary Isentropic-Coordinate (EPIC) atmospheric model. Icarus 132 (1998) 221-238
18. Dritschel D., and Ambaum M. A contour-advective semi-Lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields. Q. J. R. Meteor. Soc. 123 (1997) 1097-1130
19. Gammie C. Layered accretion in T Tauri disks. Astrophys. J. 457 (1996) 355-362
20. Gilman P., and Glatzmaier G. Compressible convection in a rotating spherical shell. I. Anelastic equations. Astrophys. J., Suppl. Ser. 45 (1981) 335-349
21. Givoli D. Non-reflecting boundary conditions. J. Comput. Phys. 94 (1991) 1-29
22. Goldreich P., and Lynden-Bell D. I. Gravitational stability of uniformly rotating disks. Mon. Not. R. Astron. Soc. 130 (1965) 97-124
23. Gottlieb D., and Orszag S. Numerical Analysis of Spectral Methods: Theory and Applications (1977), Society for Industrial and Applied Mathematics, Philadelphia
24. Gough D. The anelastic approximation for thermal convection. J. Atmos. Sci. 26 (1969) 448-456
25. Kida S. Motion of an elliptic vortex in a uniform shear flow. J. Phys. Soc. Jpn. 50 10 (1981) 3517-3520
26. -1) time step restriction. J. Comput. Phys. 104 (1993) 457-469
27. Kundu P. Fluid Mechanics (1990), Academic Press, San Diego
28. Macaskill C., Padden W., and Dritschel D. The CASL algorithm for quasi-geostrophic flow in a cylinder. J. Comput. Phys. 188 (2003) 232-251
29. Marcus P. Simulation of Taylor-Couette flow. I. Numerical methods and comparison with experiment. J. Fluid Mech. 146 (1984) 45-64
30. Marcus P. Description and philosophy of spectral methods. In: Winkler K.-H., and Norman M. (Eds). Proceedings of Astrophysical Radiation Hydrodynamics (1986), Springer, Berlin 359-386
31. Marcus P. Vortex dynamics in a shearing zonal flow. J. Fluid Mech. 215 (1990) 393-430
32. Marcus P. Jupiter's Great Red Spot and other vortices. Annu. Rev. Astron. Astrophys. 31 (1993) 523-573
33. Marcus P., and Press W. On Green's functions for small disturbances of plane Couette flow. J. Fluid Mech. 79 (1977) 525-534
34. Miesch M., Elliott J., Toomre J., Clune T., Glatzmaier G., and Gilman P. Three-dimensional spherical simulations of solar convection. I. Differential rotation and pattern evolution achieved with laminar and turbulent states. Astrophys. J. 532 (2000) 593-615
35. Mohebalhojeh A., and Dritschel D. Contour-advective semi-Lagrangian numerical algorithms for many-layer primitive equation models. Q. J. R. Meteor. Soc. 130 (2004) 347-364
36. Moore D., and Saffman P. Structure of a line vortex in an imposed strain. In: Olsen J.H., Goldburg A., and Rogers H. (Eds). Aircraft Wake Turbulence and its Detection (1971), Plenum Press, New York 339-354
37. Ogura Y., and Phillips N. Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci. 19 (1962) 73-79
38. Pedlosky J. Geophysical Fluid Dynamics (1979), Springer, New York
39. R. Rogallo, Numerical experiments in homogeneous turbulence, Technical memorandum 81315, NASA, 1981.
40. J. Stone, 2006. Available from: .
41. Stone J., and Norman M. ZEUS-2D: a radiation magnetohydrodynamics code for astrophysical flows in two space dimensions: I. The hydrodynamic algorithms and tests. Astrophys. J., Suppl. Ser. 80 (1992) 753
42. Stone J., and Norman M. ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions: II. The magnetohydrodynamic algorithms and tests. Astrophys. J., Suppl. Ser. 80 (1992) 791
43. Stone J., and Norman M. ZEUS-2D: a radiation magnetohydrodynamics code for astrophysical flows in two space dimensions: III. The radiation hydrodynamic algorithms and tests. Astrophys. J., Suppl. Ser. 80 (1992) 819
44. Velikhov E. Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field. Sov. Phys. JETP 36 (1959) 1398-1404