Sediment transport in turbulent flows with the lattice Boltzmann method

Abstract

The burial and scour of objects at the bottom of the ocean is governed by a range of different factors and is thus a complex system to simulate with numerical methods. In this work, we present a sediment transport model based on the lattice Boltzmann method which is capable of predicting the influence of a unidirectional flow field on the development of the sand bed in the vicinity of arbitrarily shaped objects, even under turbulent conditions and relatively low resolution. The underlying lattice Boltzmann method for the fluid phase of the simulation is governed by the three-dimensional entropic multi-relaxation time collision model and further makes use of appropriate three-dimensional grid refinement and off-lattice boundaries. The corresponding framework was implemented in the open-source Palabos library and enables accurate turbulent flow simulations around arbitrarily shaped objects without the need to tune any specific model parameters. For the simulation of the sediment transport, the advection–diffusion equation is solved via the lattice Boltzmann method with an adapted version of the entropic multi-relaxation time collision model for a three-dimensional lattice with seven discrete lattice velocities (D3Q7). The presented sediment transport model thus inherits the unconditional numerical stability and the simplicity of the entropic multi-relaxation time collision model. Furthermore, erosion and sedimentation processes are included based on the critical Shields parameter, i.e. on the wall shear stress. An initial simulation of the flow and sediment transport around a horizontally bedded finite cylinder shows that the presented model is generally able to capture the major sediment processes which govern the development of the sand bed.