Computational Geosciences

, Volume 19, Issue 4, pp 965–978 | Cite as

Multilevel and local time-stepping discontinuous Galerkin methods for magma dynamics

  • S. TirupathiEmail author
  • J. S. Hesthaven
  • Y. Liang
  • M. Parmentier


Discontinuous Galerkin (DG) method is presented for numerical modeling of melt migration in a chemically reactive and viscously deforming upwelling mantle column at local chemical equilibrium. DG methods for both advection and elliptic equations provide a robust and efficient solution to the problems of melt migration in the asthenospheric upper mantle. Assembling and solving the elliptic equation is the major bottleneck in these computations. To address this issue, adaptive mesh refinement and local time-stepping methods have been proposed to improve the computational wall time. The robustness of DG methods is demonstrated through two benchmark problems by modeling detailed structure of high-porosity dissolution channels and compaction dissolution waves.


Numerical solutions Discontinuous Galerkin Adaptive mesh refinement Local time-stepping Mid-ocean ridge processes Magma migration Physics of magma bodies 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • S. Tirupathi
    • 1
    • 4
    Email author
  • J. S. Hesthaven
    • 2
  • Y. Liang
    • 3
  • M. Parmentier
    • 3
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Mathematics Institute of Computational Science and Engineering, EPFLLausanneSwitzerland
  3. 3.Department of Earth, Environmental and Planetary SciencesBrown UniversityProvidenceUSA
  4. 4.IBM Research - IrelandDublinIreland

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