Can we obtain a well balanced property in the 2D shallow water with topography with second order accuracy and Roe's scheme on unstructured grid?

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Chinedu Nwaigwe

Yes, this is possible. You can use the hydrostatic reconstruction scheme which allows you to use numerical flux solver of your choice (Roe in this case). See the link Article A Fast and Stable Well-Balanced Scheme with Hydrostatic Reco...

Abdelkader Mohamed Elsayed

This Link Maybe Useful:

https://www.sciencedirect.com/science/article/pii/S0021999117300190