This paper deals with the modelling and simulation of segregation in granular materials. The basis is a hydrodynamic model for granular material flows, which is extended to capture the dynamic process of segregation in shear flows of systems with small and large particles. The granular flow equations consist of a set of compressible Navier–Stokes-like equations as well as an equation for the granular temperature. With the help of the granular temperature equation, the granular flow equations are able to cover a wide range of regimes, starting from dilute to arresting flows. However, this paper focuses on dry granular shear flows. It extends this hydrodynamic system in a dense shear flow regime by a segregation equation using the framework of mixture theory. Special focus is lain on the segregation direction. A procedure from mechanics is adapted to obtain the segregation direction from the granular flow system independent of the choice of the coordinate system. In particular, this is done in three-dimensional space. Due to the compressibility of the granular flow system and the structure of the derived segregation equation, solving the segregation equation requires special numerical treatment. Therefore, a suitable numerical scheme is presented which prevents the system from reaching unphysical states.

中文翻译：

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二元颗粒系统可压缩颗粒剪切流中的尺寸偏析

本文涉及粒状材料中偏析的建模和模拟。该基础是用于颗粒状物料流的流体动力学模型，该模型被扩展为捕获大小颗粒系统的剪切流中偏析的动态过程。颗粒流动方程由一组可压缩的Navier–Stokes式方程以及颗粒温度方程组成。借助颗粒温度方程，颗粒流动方程能够涵盖从稀流到阻滞流的各种状态。但是，本文着重于干颗粒剪切流。它使用混合理论的框架通过偏析方程在稠密的剪切流动状态下扩展了该水动力系统。特别关注的是隔离方向。来自力学的过程适于独立于坐标系的选择而从粒状流系统获得偏析方向。特别地，这是在三维空间中完成的。由于颗粒流系统的可压缩性和导出的偏析方程的结构，解决偏析方程需要特殊的数值处理。因此，提出了一种合适的数值方案，可以防止系统达到非物理状态。