A Boltzmann based model for open channel flows

A finite volume, Boltzmann Bhatnagar-Gross-Krook (BGK) numerical model for one- and two-dimensional unsteady open channel flows is formulated and applied. The BGK scheme satisfies the entropy condition and thus prevents unphysical shocks. In addition, the van Leer limiter and the collision term ensure that the BGK scheme admits oscillation-free solutions only. The accuracy and efficiency of the BGK scheme are demonstrated through the following examples: (i) strong shock waves, (ii) extreme expansion waves, (iii) a combination of strong shock waves and extreme expansion waves, and (iv) one-and two-dimensional dam break problems. These test cases are performed for a variety of Courant numbers (C r ), with the only condition being C r < 1. All the computational results are free of spurious oscillations and unphysical shocks (i.e., expansion shocks)

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