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

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Abstract

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.

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Acknowledgements

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

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Authors and Affiliations

  1. Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA, USA

    Savithru Jayasinghe, David L. Darmofal, Marshall C. Galbraith & Steven R. Allmaras

  2. Aramco Services Company, 400 Technology Square, Cambridge, MA, USA

    Nicholas K. Burgess

Authors
  1. Savithru Jayasinghe
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  2. David L. Darmofal
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  3. Nicholas K. Burgess
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  4. Marshall C. Galbraith
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  5. Steven R. Allmaras
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Corresponding author

Correspondence to Savithru Jayasinghe.

Additional information

This research was supported through a Research Agreement with Saudi Aramco, a Founding Member of the MIT Energy Initiative (http://mitei.mit.edu/), with technical monitors Dr. Ali Dogru and Dr. Nicholas Burgess.

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Jayasinghe, S., Darmofal, D.L., Burgess, N.K. et al. A space-time adaptive method for reservoir flows: formulation and one-dimensional application. Comput Geosci 22, 107–123 (2018). https://doi.org/10.1007/s10596-017-9673-9

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