Estimation of the role of obstacles in the downslope soil flow with a simple erosion model: the analytical solution and its approximation with the lattice Boltzmann model

The description of a downslope soil particle flow is usually assumed to be uniform. Nevertheless, the presence of obstacles like stones, rock outcrops or plants hinders the uniformity of the flow. Culling, in 1983, proposed an analytical solution for the advective–dispersive flow of soil particles around circular and elliptical cross section obstacles. In this paper, the Culling solution is extended using a more versatile numerical method based on the integration of the transport equations at the mesoscopic level, the lattice Boltzmann model (LBM). Ms are used for the description of the flow components. The first LBM simulates the advection component and the second one the diffusion component. The distribution of soil or any tracer particles produced by the model is similar to the prediction of the analytical solution. The LBM has a greater flexibility for the study of intricate geometries allowing more irregular boundary conditions closer to field situations. The model has been applied to the analysis of the flow of soil or any tracer particles around several obstacles such as the trunks in a forest or a regular plantation.