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BGK based finite volume scheme for hydraulic applications

This paper explores some of the applications of Boltzmann models in the hydraulic field. A finite volume scheme with fluxes evaluated based on the solution of the Bhatnagar–Gross-Krook (BGK) Boltzmann equation for surface water flows is obtained. The consistency of the BGK equation with the classical mass and momentum equations for shallow water flow in two-lateral dimensional systems is shown. Turbulence models are incorporated through the collision time. The model is applied to a wide range of problems in surface water hydraulics including circular dam break (bore), roll waves, shallow wakes and shallow mixing layers. Where possible, model results are compared to experimental data.