Stable and Efficient Time Integration of a Dynamic Pore Network Model for Two-Phase Flow in Porous Media

@article{Gjennestad2018StableAE,
  title={Stable and Efficient Time Integration of a Dynamic Pore Network Model for Two-Phase Flow in Porous Media},
  author={Magnus Aa. Gjennestad and Morten Vassvik and Signe Kjelstrup and Alex Hansen},
  journal={Frontiers in Physics},
  year={2018}
}
We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method developed herein. The explicit methods are known to suffer from numerical instabilities at low capillary numbers. A new time-step criterion is suggested in order to stabilize them. Numerical experiments, including a Haines jump case, are performed and these… 

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