A Fully Mass and Volume Conserving Implementation of a Characteristic Method for Transport Problems

@article{Arbogast2006AFM,
  title={A Fully Mass and Volume Conserving Implementation of a Characteristic Method for Transport Problems},
  author={Todd Arbogast and Chieh-Sen Huang},
  journal={SIAM J. Sci. Comput.},
  year={2006},
  volume={28},
  pages={2001-2022}
}
The characteristics-mixed method considers the transport not of a single point or fluid particle, but rather the mass in an entire region of fluid. This mass is transported along the characteristic curves of the hyperbolic part of the transport equation, and the scheme thereby produces very little numerical dispersion, conserves mass locally, and can use long time steps. However, since the shape of a characteristic trace-back region must be approximated in numerical implementation, its volume… 

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