New models for geophysical mass flows
Le, Long Hoang
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Granular flow is a common concept in studying geophysical mass flows. Volcanic avalanches, mud flows, landslides or debris flows can be considered to be granular flows or granular-fluid mixture flows. The range of scales and the complexity of the rheology for geological materials, coupled with the mathematical problem of describing a free surface flow, makes modeling and computing geophysical mass flows a significant challenge. My thesis consists of two different aspects of modeling mass flows. First, we have developed a new model for mass flows over an erodible layer that includes changes to the topography over which the mass is moving. In the models without erosion, there is no interaction between the moving mass and the bed. Some approaches to model erosion assume a frozen bed, which basically means that although the flow erodes material from the bed, the change is negligible. In our model, we assume there is a very thin mixing layer between the moving mass and the erodible surface, in which the erodible material gains the necessary velocity to enter the flow above. We use a rapid flow theory for this mixing layer to obtain an appropriate boundary condition at the interface between the moving flow and the erodible layer, and then use it to compute the changes of the erodible ground. Second, we have developed a new model for two-phase flows, overcoming some of the challenges to the Iverson's mixture model at the expense of introducing a more complex set of equations. In our model, we are able to consider separate phases of fluid and solid. Although we include only the simplest of phase interactions, the model provides a sufficiently rich description of solid and fluid phases while still being amenable to mathematical analysis. Both models are developed through depth-averaging process. We have showed that both models are hyperbolic, which is important in order to obtain a numerical solution.