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High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation
Journal of Non-Newtonian Fluid Mechanics ( IF 3.1 ) Pub Date : 2021-05-03 , DOI: 10.1016/j.jnnfm.2021.104556
J.R.C. King , S.J. Lind

Viscoelastic flows occur widely, and numerical simulations of them are important for a range of industrial applications. Simulations of viscoelastic flows are more challenging than their Newtonian counterparts due to the presence of exponential gradients in polymeric stress fields, which can lead to catastrophic instabilities if not carefully handled. A key development to overcome this issue is the log-conformation formulation, which has been applied to a range of numerical methods, but not previously applied to Smoothed Particle Hydrodynamics (SPH). Here we present a 2D incompressible SPH algorithm for viscoelastic flows which, for the first time, incorporates a log-conformation formulation with an elasto-viscous stress splitting (EVSS) technique. The resulting scheme enables simulations of flows at high Weissenberg numbers (accurate up to Wi=85 for Poiseuille flow). The method is robust, and able to handle both internal and free-surface flows, and a range of linear and non-linear constitutive models. Several test cases are considered including flow past a periodic array of cylinders and jet buckling. This work presents a significant step change in capabilities compared to previous SPH algorithms for viscoelastic flows, and has the potential to simulate a wide range of new and challenging applications.



中文翻译:

具有不可压缩平滑粒子流体动力学和对数构象公式的高 Weissenberg 数模拟

粘弹性流动广泛发生,它们的数值模拟对于一系列工业应用很重要。由于聚合物应力场中存在指数梯度,粘弹性流动的模拟比牛顿模拟更具挑战性,如果处理不当,可能会导致灾难性的不稳定性。克服这个问题的一个关键发展是对数构象公式,它已应用于一系列数值方法,但以前未应用于平滑粒子流体动力学 (SPH)。在这里,我们提出了一种用于粘弹性流动的二维不可压缩 SPH 算法,该算法首次将对数构象公式与弹性粘性应力分裂 (EVSS) 技术相结合。由此产生的方案能够模拟高魏森伯格数(精确到一世=85泊肃叶流)。该方法是稳健的,能够处理内部和自由表面流动,以及一系列线性和非线性本构模型。考虑了几个测试案例,包括流过周期性圆柱阵列和喷射屈曲。与以前用于粘弹性流动的 SPH 算法相比,这项工作在功能上发生了重大变化,并且有可能模拟各种新的和具有挑战性的应用。

更新日期:2021-06-02
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