Particle models for sand transport in water: analysis and simulations

Abstract

This thesis describes how the simple random walk particle model can be extended to account for sand deposition and suspension, and for particle interaction: clumping together and falling apart. The extended models are analyzed, and the corresponding partial differential equations are derived. These equations are compared to the currently used transport equations. The majority of the analysis is about particle interaction, for which a stochastic differential equation for mass was added to the random walk model. The resulting equation for the particle number density is not in complete agreement with the one that is currently used, due to the choice of the mass equation.

Furthermore, numerous simulations are done using both the basic models and the extended ones. The simulation results were as expected. Several comparisons are made between the random walk model and the random flight model, and between models with and without the extensions described. For these comparisons too, the results were as expected.

Recommendations for further research include simulating with more realistic conditions and domains, and developing a more advanced model extension for particle interaction. Also, the effects of particle interaction on particle deposition and suspension could be analyzed, as this thesis does not cover an extended model for both effects.