Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients

@article{Chertock2014CentralupwindSF,
  title={Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients},
  author={Alina Chertock and Alexander Kurganov and Yu Liu},
  journal={Numerische Mathematik},
  year={2014},
  volume={127},
  pages={595-639}
}
We introduce a central-upwind scheme for one- and two-dimensional systems of shallow-water equations with horizontal temperature gradients (the Ripa system). The scheme is well-balanced, positivity preserving and does not develop spurious pressure oscillations in the neighborhood of temperature jumps, that is, near the contact waves. Such oscillations would typically appear when a conventional Godunov-type finite volume method is applied to the Ripa system, and the nature of the oscillation is… 
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