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 appl ied. The BGK scheme satisfies the entropy condition and thus prevents unphy sical shocks. In addition, the van Leer limiter and the collision term ensu re that the BGK scheme admits oscillation-free solutions only. The accuracy and efficiency of the BGK scheme are demonstrated through the following ex amples: (i) strong shock waves, (ii) extreme expansion waves, (iii) a combi nation of strong shock waves and extreme expansion waves, and (iv) one- and two-dimensional dam break problems. These test cases are performed for a v ariety of Courant numbers (C-r), with the only condition being C(r)less tha n or equal to1. All the computational results are free of spurious oscillat ions and unphysical shocks (i.e., expansion shocks). In addition, compariso ns of numerical tests with measured data from dam break laboratory experime nts show good agreement for C(r)less than or equal to0.6. This reduction in the stability domain is due to the explicit integration of the friction te rm. Furthermore, BGK schemes are easily extended to multidimensional proble ms and do not require characteristic decomposition. The proposed scheme is second-order in both space and time when the external forces are zero and s econd-order in space but first-order in time when the external forces are n on-zero. However, since all the test cases presented are either for zero or small values of external forces, the results tend to maintain second-order accuracy. In problems where the external forces become significant, it is possible to improve the order of accuracy of the scheme in time by, for exa mple, applying the Runge-Kutta method in the integration of the external fo rces. Copyright (C) 2001 John Wiley & Sons, Ltd.