论文标题
具有不可压缩的平滑粒子流体动力学和对数符合配方的高魏森贝格数字模拟
High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation
论文作者
论文摘要
粘弹性流广泛发生，它们的数值模拟对于一系列工业应用很重要。由于在聚合应力场中存在指数梯度，粘弹性流的模拟比其牛顿的模拟更具挑战性，如果不仔细处理，这可能导致灾难性不稳定。克服此问题的一个关键发展是对数构成公式，该公式已应用于一系列数值方法，但以前不应用于平滑的粒子流体动力学（SPH）。在这里，我们提出了一种用于粘弹性流的2D不可压缩的SPH算法，该算法首次结合了与弹性粘性应力分裂（EVSS）技术的对数结构配方。最终的方案可以模拟在高魏森伯格数字上的流量（Poiseuille流量为85 = 85）。该方法是鲁棒的，并且能够处理内部和自由表面流以及一系列线性和非线性本构模型。考虑到几个测试用例包括经过周期性的气缸和喷气屈曲的流量。与以前的SPH算法相比，这在粘弹性流动中呈现了重大的步骤变化，并且有可能模拟广泛的新型和具有挑战性的应用。
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 considerd included flow past a periodic array of cylinders and jet buckling. This presents a significant step change in capabilties compared to previous SPH algorithms for viscoelastic flows, and has the potential to simulate a wide range of new and challenging applications.
