One-dimensional mathematical modeling of flow and sediment transport in open channels using the lattice Boltzmann method

Abstract

A one-dimensional unsteady open-channel flow with sediment transport lattice Boltzmann model is developed. The unsteady water flow model is based on the discharge-water level definition of the Saint-Venant equations. For the sediment active-layer concept is used. Geometrical transformations are applied to the governing equations, in order to transform non-uniform physical spatial grid, characteristic for natural geometry, into an uniform computational grid. New form of equilibrium distribution functions is derived. Bifurcation boudary conditions suitable with the lattice Bolcmann method are derived. Verification of the proposed model is obtained by testing unsteady flow model on three cases: steday flow in a prismatic channel, usteady flow in an unprismatic channel and unsteady flow in a natural watercourse – Danube River case study. Sediment transport model is tested on two cases: advection-diffusion in a prismatic channel and unsteady flow with sediment transport in a natural watercouse – Danube River case study.