Computational Geosciences

, Volume 22, Issue 1, pp 107–123 | Cite as

A space-time adaptive method for reservoir flows: formulation and one-dimensional application

  • Savithru Jayasinghe
  • David L. Darmofal
  • Nicholas K. Burgess
  • Marshall C. Galbraith
  • Steven R. Allmaras
Original Paper


This paper presents a space-time adaptive framework for solving porous media flow problems, with specific application to reservoir simulation. A fully unstructured mesh discretization of space and time is used instead of a conventional time-marching approach. A space-time discontinuous Galerkin finite element method is employed to achieve a high-order discretization on the anisotropic, unstructured meshes. Anisotropic mesh adaptation is performed to reduce the error of a specified output of interest, by using a posteriori error estimates from the dual-weighted residual method to drive a metric-based mesh optimization algorithm. The space-time adaptive method is tested on a one-dimensional two-phase flow problem, and is found to be more efficient in terms of computational cost (degrees-of-freedom and total runtime) required to achieve a specified output error level, when compared to a conventional first-order time-marching finite volume method and the space-time discontinuous Galerkin method on structured meshes.


Unstructured space-time methods Anisotropic mesh adaptation Discontinuous Galerkin High-order Two-phase flow 


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The authors wish to thank Dr. Eric Dow for reviewing this paper.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Savithru Jayasinghe
    • 1
  • David L. Darmofal
    • 1
  • Nicholas K. Burgess
    • 2
  • Marshall C. Galbraith
    • 1
  • Steven R. Allmaras
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.Aramco Services CompanyCambridgeUSA

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