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.