Numerical implementation of streaming down the gradient: Application to fluid modeling of cosmic rays and saturated conduction

SIAM Journal on Scientific Computing

Volumn 32, Issue 6, 2010, Pages 3564-3583

  Sharma, Prateek ^a   Colella, Phillip ^b   Martin, Daniel F ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

Finite differencing; Implicit methods; Monotonicity

Indexed keywords

ADVECTION; COLLISIONLESS PLASMAS; COSMIC RAYS; COSMOLOGY; NUMERICAL METHODS;

ADVECTION EQUATIONS; COMPUTATIONAL DOMAINS; EXPLICIT METHOD; FINITE DIFFERENCING; FLUID MODELING; IMPLICIT METHODS; LOCAL EXTREMUM; MONOTONICITY; NUMERICAL IMPLEMENTATION; TIME STEP;

NONLINEAR EQUATIONS;

EID: 79251512983     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/100792135     Document Type: Article

References (18)

1. S. A. Balbus, Magnetized Thermal Conduction Fronts, Astrophys. J., 304 (1986), pp. 787-798.
2. D. S. Balsara, D. A. Tilley, and J. C. Howk, Simulating anisotropic thermal conduction in supernova remnants-I, Numerical Methods, Monthly Not. R. Astron. Soc., 386 (2008), pp. 627-641.
3. A. R. Bell, Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays, Monthly Not. R. Astron. Soc., 353 (2004), pp. 550-558.
4. A. Boulares and D. P. Cox, Galactic hydrostatic equilibrium with magnetic tension and cosmic-ray diffusion, Astrophys. J., 365 (1990), pp. 544-558.
5. F. Guo and S. P. Oh, Feedback heating by cosmic rays in clusters of galaxies, Monthly Not. R. Astron. Soc., 384 (2008), pp. 251-266.
6. R. M. Kulsrud, Plasma Physics for Astrophysics, Princeton University Press, Princeton, NJ, 2005.
7. P. Lax and B. Wendroff, Systems of conservation laws, Comm. Pure App. Math., 13 (1960),pp. 217-237.
8. R. J. Leveque, Finite Volume Methods for Hyperbolic Problems, Cambridge Univeristy Press, London, 2002.
9. M. Loewenstein, E. G. Zweibel, and M. C. Begelman, Cosmic-ray heating of cooling flows: A critical analysis, Astrophys. J., 377 (1991), pp. 392-402.
10. J. F. McKenzie and Völk, Nonlinear theory of cosmic ray shocks inducing self-generated Alfven waves, Astronom. Astrophys., 116 (1982), pp. 191-200.
11. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, London, 1992.
12. Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869.
13. P. Sharma and G. W. Hammett, Preserving monotonicity in anisotropic diffusion, J. Comput. Phys., 227 (2007), pp. 123-142.
14. P. Sharma and G. W. Hammett, A fast semi-implicit method for anisotropic diffusion, 2010, arXiv:1008.0861.
15. P. Sharma, B. D. G. Chandran, E. Quataert, and I. J. Parrish, Buoyancy instabilities in galaxy clusters: Convection due to adiabatic cosmic rays and anisotropic thermal conduction, Astrophys. J., 699 (2009), pp. 348-361.
16. B. van Leer, Towards the ulitmate conservative difference scheme. IV. A new approach to numerical convection, J. Comput. Phys., 23 (1977), pp. 276-299.
17. D. G. Wentzel, Acceleration and heating of interstellar gas by cosmic rays, Astrophys. J., 163 (1971), pp. 503-514.
18. H. Yan and A. Lazarian, Cosmic-ray scattering and streaming in compressive magnetohydrodynamic turbulence, Astrophys. J., 614 (2004), pp. 757-769.