Computational Methods for Bulk Solid Handling Problems

尽管已经提出了许多连续介质模型，但颗粒材料的力学行为仍然只是部分地被理解。该项目的目标是建立、研究、实施和测试高效可靠的数值方法，以便对这些模型进行定量研究和比较。具体研究的问题包括波在块状材料中的传播、静态颗粒堆、细粉的多相模型和多维颗粒流。在所有这些问题中，干摩擦起着核心作用。根据问题及其公式的不同，摩擦效应的存在在数学上以各种方式表现出来：图的存在、平衡定律系统中的刚性源项、代数约束。每一个困难都会带来新的数字挑战。由上述现象的模型化而产生的各种各样的数学问题（微分包含、守恒定律系统、平衡定律、汉密尔顿-雅可比方程、椭圆和抛物问题、非局部自由边界问题）证明了这个领域令人难以置信的丰富性。在无数的行业中，物料必须以颗粒形式进行加工、储存和回收。令人惊讶的是，在这些不同的阶段会出现许多问题。困难的范围从卸料时筒仓的完全结构倒塌到生产过程的性能差和不可预测性。这给固体加工厂带来了非常高的财务成本。在与学术界和工业界的工程师协商后，建议设计和实施允许在一般几何中计算颗粒流动和相关问题的数值方法。目前使用的方法可以追溯到20世纪50年代，预测能力有限。

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.