We employ kinetic theory, extended to incorporate the influence of velocity correlations, friction and particle stiffness, and a model for rate-independent, elastic components of the stresses at volume fractions larger than a critical value, in an attempt to reproduce the results of discrete-element numerical simulations of steady, fully developed, dissipative, collisional shearing flows over and within inclined, erodible, fragile beds. The flows take place between vertical, frictional sidewalls at different separations with sufficient total particle flux so that differently inclined, erodible beds result. Numerical solutions of the spanwise-averaged differential equations of the theory and the associated boundary conditions are seen to be capable of reproducing profiles of stresses, solid volume fraction, average velocity and the strength of the particle velocity fluctuations, both in the rapid collisional flow above the bed and in the slower creeping flow within the bed. The indication is that extended kinetic theory has the unique ability to faithfully describe steady, inhomogeneous, granular shearing flows, ranging from dilute to extremely dense, using balances of momentum and energy and employing boundary conditions that are associated with the balances, with a small number of physically determined, microscopic parameters.

中文翻译：

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倾斜可蚀床上方和内部颗粒流的扩展动力学理论

我们采用动力学理论，扩展到结合速度相关性、摩擦和粒子刚度的影响，以及在体积分数大于临界值时应力的与速率无关的弹性分量模型，试图重现离散的结果对倾斜、易蚀、脆弱的床层上方和内部的稳定的、完全发展的、耗散的、碰撞的剪切流的元素数值模拟。流动发生在不同间隔处的垂直摩擦侧壁之间，具有足够的总颗粒通量，从而产生不同倾斜的可侵蚀床。理论的展向平均微分方程和相关边界条件的数值解被认为能够再现应力、固体体积分数、平均速度和粒子速度波动的强度，无论是在床层上方的快速碰撞流中，还是在床层内较慢的蠕动流中。这表明扩展动力学理论具有独特的能力，可以使用动量和能量的平衡以及与平衡相关的边界条件，如实描述稳定的、不均匀的、粒状剪切流，范围从稀到极密。物理确定的微观参数。