Computational Methods for Bulk Solid Handling Problems

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The mechanical behavior of granular materials is still only partially undertsood even though many continuum models have been proposed. The goal of this project is to build, study, implement and test efficient and reliable numerical methods allowing for a quantitative study and comparison of those models. Specific problems to be studied include wave propagation in bulk materials, static granular piles, multiphase models for fine powders and multidimensional granular flows. In all those problems, dry friction plays a central role. Depending on the problem and its formulation, the presence of frictional effects manifests itself mathematically in various ways: presence of a graph, stiff source term in systems of balance laws, algebraic constraints. Each of those difficulties leads to new numerical challenges. The wide variety of mathematical problems resulting from the modelization of the above phenomena (differential inclusion, systems of conservation laws, balance laws, Hamilton-Jacobi equations, elliptic and parabolic problems, non-local free boundary problems) is a testimony to the incredible richness of this field.In countless industries, materials have to be processed, stored and retrieved in granular form. Surprisingly many problems occur during those various phases. Difficulties range from the complete structural collapse of silos during discharge to poor performance and unpredictability of the manufacturing process. This comes at a very high financial cost to solid processing plants. It is proposed to design and implement, in consultation with engineers from both Academia and Industry, numerical methods that allow for the calculations of granular flows and related problems in general geometries. The current methods in use date back to the 1950's and have limited predicitive capabilities.