Modeling magma dynamics with a mixed Fourier collocation-discontinuous Galerkin method

Communications in Computational Physics

Volumn 10, Issue 2, 2011, Pages 433-452

  Schiemenz, Alan R ^a,c   Hesse, Marc A ^b   Hesthaven, Jan S ^a  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c UNIVERSITY OF MUNICH   (Germany)

Author keywords

Discontinuous Galerkin method; Fourier collocation method; Linear stability analysis; Magma dynamics; Numerical simulations

Indexed keywords

EID: 79955660417     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.030210.240910a     Document Type: Article

References (13)

1. E. Aharonov, J. Whitehead, P. B. Kelemen and M. Spiegelman, Channeling instability of upwelling melt in the mantle, J. Geophys. Res., 100(1995), 433-450.
2. D. N. Arnold, F. Brezzi, B. Cockburn and L. D. Marini, Unified analysis of discontinuous galerkin methods for elliptic problems, SIAM J. Numer. Anal., 39(2002), 1749-1779.
3. D. Bercovici, Y. Ricard and G. Schubert, A two-phase model for compaction and damage 1. General theory, J. Geophys. Res., 106(2001), 8887-8906.
4. O. Buneman, Diagnosing oscillatory growth or decay, J. Comput. Phys., 29(1978), 295-296.
5. M. H. Carpenter and C. A. Kennedy, Fourth-order 2N-storage Runge-Kutta schemes, NASA TM 109112, NASA Langley Research Center, 1994.
6. M. A. Hesse, A. R. Schiemenz, Y. Liang and E. M. Parmentier, Compaction-dissolution waves in an upwelling mantle column, Geophys. J. Int., 2011 (submitted).
7. J. S. Hesthaven, S. Gottlieb and D. Gottlieb, Spectral Methods for Time-Dependent Problems, Cambridge University Press, 2006.
8. J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, Springer, 2008.
9. P. B. Kelemen, G. Hirth, N. Shimizu, M. Spiegelman and H. J. B. Dick, A review of melt migration processes in the adiabatically upwelling mantle beneath oceanic spreading ridges, Phil. Trans. R. Soc. Lond., 355(1997), 282-318.
10. Y. Saad, Iterative Methods for Sparse Linear Systems (2nd edition), SIAM Publishing, 2003.
11. A. R. Schiemenz, Y. Liang and E. M. Parmentier, A high-order numerical study of reactive dissolution in an upwelling heterogenous mantle: I. Channelization, channel lithology, and channel geometry, Geophys. J. Int., 2010 (in revision).
12. M. Spiegelman and P. B. Kelemen, Extreme chemical variability as a consequence of channelized melt transport, Geochem. Geophys. Geosyst., 4(7) (2003), 1055.
13. M. Spiegelman, P. B. Kelemen and E. Aharonov, Causes and consequences of flow organization during melt transport: The reaction infiltration instability in compactible media, J. Geo. Res., 106(2001), 2061-2077.