The current paper is focused on analyzing the flow of viscoplastic fluid in a cavity that is driven by the two walls. The Lattice Boltzmann method (LBM) is used to solve the discrete Boltzmann equation. To represent the stress-strain rate relationship of viscoplastic fluids, the Bingham Papanastasiou constitutive model is considered. Cavity flow filled with Bingham fluids is considered for validating the present LBM code. After successful validation of the code, the analysis is extended for three dissimilar wall motions-simultaneous and opposed movement of the parallel facing walls, and the simultaneous motion of non-facing walls. The flow dynamics of Bingham fluid is influenced by Reynolds and Bingham numbers which can be studied using velocity and streamline plots. Subsequently, the yielded and un-yielded zones in a cavity have been effectively tracked using the limiting condition of yield stress. Further, the effect of wall motion on the variation of those zones inside a cavity has been studied. Finally, the drag coefficient for considered wall motions is presented.

中文翻译：

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用莱迪思·玻尔兹曼方法模拟壁运动引起的腔内粘塑性流体的流动

本论文的重点是分析由两个壁驱动的空腔中的粘塑性流体的流动。格子Boltzmann方法（LBM）用于求解离散Boltzmann方程。为了表示粘塑性流体的应力-应变率关系，考虑了Bingham Papanastasiou本构模型。考虑用充满宾厄姆流体的腔流来验证当前的LBM代码。在成功验证代码之后，将分析扩展到三个不同的壁运动，即平行面对壁的同时和相对运动，以及非面对壁的同时运动。宾汉流体的流动动力学受雷诺数和宾汉数的影响，可以使用速度和流线图对其进行研究。后来，利用屈服应力的极限条件，可以有效地跟踪型腔中的屈服区和非屈服区。此外，已经研究了壁运动对腔体内那些区域的变化的影响。最后，给出了考虑壁运动的阻力系数。