Skip to main content Accessibility help

Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method

  • Seshu Tirupathi (a1) (a2), Jan S. Hesthaven (a1) (a3) and Yan Liang (a4)


Discontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical modeling of magma dynamics in 2D and 3D using the library deal.II. The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance at local chemical equilibrium and one elliptic equation to recover global pressure. A combination of a discontinuous Galerkin method for the advection equations and a finite element method for the elliptic equation provide a robust and efficient solution to the channel regime problems of the physical system in 3D. A projective and adaptively applied pressure estimation is employed to significantly reduce the computational wall time without impacting the overall physical reliability in the modeling of important features of melt segregation, such as melt channel bifurcation in 2D and 3D time dependent simulations.


Corresponding author

*Corresponding author. Email addresses: (S. Tirupathi), (J. S. Hesthaven), (Y. Liang)
Current address: IBM Research, Dublin, Damastown Industrial Park, Mulhuddart, Dublin 15, Ireland


Hide All
[1]Abreu, E., Douglas, J., Furtado, F. and Pereira, F., Operator splitting for three-phase flow in heterogeneous porous media, Commun. Comput. Phys., 6 (2009), 7284.
[2]Aharonov, E., Whitehead, J., Kelemen, P. B. and Spiegelman, M. S, Channeling instability of upwelling melt in the mantle, J. Geophys. Res., 100 (1995), 2043320450.
[3]Bangerth, W., Hartmann, R. and Kanschat, G., deal.II: A general-purpose object-oriented finite element library, ACM Transactions on Mathematical Software, 33 (2007), 127.
[4]Buneman, O., Diagnosing oscillatory growth or decay, J. Comput. Phys., 29 (1978), 295296.
[5]Carpenter, M. H. and Kennedy, C. A.Fourth-order 2N-storage Runge-Kutta schemes, NASA TM 109112, NASA Langley Research Center, 1994.
[6]Chueh, C., Djilali, N. and Bangerth, W., An h-adaptive operator splitting method for two-phase flow in 3D heterogeneous porous media, SIAM J. Sci. Comput., 35 (2013), B149B175.
[7]Hesse, M.A., Schiemenz, A. R., Liang, Y. and Parmentier, E.M., Compaction-dissolution waves in an upwelling mantle column, Geophys. J. Int., 187 (2011), 10571075.
[8]Hesthaven, J. S. and Warburton, T., Nodal discontinuous Galerkin methods: Algorithms, analysis, and applications, Springer, 2008.
[9]Kelemen, P. B., The origin of the land under the sea, Scientific American, 300 (2009), 5257.
[10]Kelemen, P. B., Hirth, G., Shimizu, N., Spiegelman, M. and Dick, H. J. B.A review of melt migration processes in the adiabatically upwelling mantle beneath oceanic spreading ridges, Phil. Trans. R. Soc. Lond., 355 (1997), 282318.
[11]Kronbichler, M. and Kormann, K., A generic interface for parallel cell-based finite element operator application, Fluids Comput., 63 (2012), 135147.
[12]Liang, Y., Schiemenz, A. R., Hesse, M., Parmentier, E. M. and Hesthaven, J.S., High-porosity channels for melt migration in the mantle: Top is the dunite and bottom is the harzburgite and lherzolite, Geophys. Res. Lett., 37 (2010), L15306.
[13]Liang, Y., Schiemenz, A. R. and Hesse, M. A.Waves, channels, and the preservation of chemical heterogeneities during melt migration in the mantle, Geophys. Res. Lett., 38 (2011), L20308.
[14]Saad, Y., Iterative methods for sparse linear systems (2nd edition), SIAM Publishing, 2003.
[15]Schiemenz, A. R., Hesse, M. A. and Hesthaven, J. S.Modeling magma dynamics with a mixed Fourier collocation – discontinuous Galerkin method, Commun. Comput. Phys., 10 (2011), 433452.
[16]Schiemenz, A. R., Liang, Y. and Parmentier, E.M., A high-order numerical study of reactive dissolution in an upwelling heterogeneous mantle: I. Channelization, channel lithology, and channel geometry, Geophys. J. Int., 186 (2011), 641664.
[17]Spiegelman, M. and Kelemen, P. B.Extreme chemical variability as a consequence of channelized melt transport, Geochem. Geophys. Geosyst., 4 (2003), 1055.
[18]Spiegelman, M., Kelemen, P. B. and Aharonov, E., Causes and consequences of flow organization during melt transport: The reaction infiltration instability in compactible media, J. Geo. Res., 106 (2001), 20612077.


MSC classification

Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method

  • Seshu Tirupathi (a1) (a2), Jan S. Hesthaven (a1) (a3) and Yan Liang (a4)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed