Author(s): Amir H. Hedjripour; David P. Callaghan; Tom E. Baldock
Keywords: Lattice Boltzmann Method; Supercritical Flow; Dam Break; Galilean Transformation
Abstract: A one-dimensional Lattice Boltzmann Model is developed to solve the shallow water equations for both subcritical and supercritical flow regimes. This addresses a major limitation of current models, which are limited to subcritical flow. A generalised Galilean transformation is applied to the standard scheme, which is equivalent to moving the standard scheme in a reference frame with constant (but not fixed) velocity. The transformation yields an asymmetric LBM scheme which can successfully model a wide range of both subcritical and supercritical flow regimes. A new set of equilibrium functions, boundary conditions and the external force weights are derived for the generalised transformed scheme. A new stability region is also defined, allowing selection of a lattice speed that maintains numerical stability for a wide range of sub-and supercritical flows and combinations of those flow conditions. The model is validated against a range of benchmark cases in open-channel hydraulics, including graduallyvaried and rapidly-varied flows and a dam break case on a horizontal frictionless bed. The results demonstrate the applicability of the new model.