剪切变稀型SPH非牛顿流体的预测-校正方法

A Predictive-Corrective SPH Method for Shear Thinning Non-Newtonian Fluid

对非牛顿流体的模拟一直是基于物理的流体模拟技术的研究难点.为解决SPH流体模拟中非牛顿流体粒子凝聚成团导致断层现象,提出一种针对剪切变稀型非牛顿流体的预测-校正方法.首先使用Cross模型对流体进行统一建模;然后计算每个流体粒子受到的除了压强力以外的其他力,以此获得中间速度;最后通过求解每个流体粒子的压强系数满足流体的不可压缩性,实现密度校正.为了提高计算速度,该方法使用全局动态时间步长.实验结果表明,文中方法实现了牛顿流体和剪切变稀型非牛顿流体的统一建模,解决了断层问题;相比于无校正方法,其能够在更大的时间步长下稳定运行.

The simulation for non-Newtonian fluid has been an important research topic in physically basedfluid animation.In this paper,we propose a novel predictive-corrective algorithm for non-Newtonian fluid based on incompressible smoothed particle hydrodynamics(ISPH).First,the viscous liquid is modeled by a non-Newtonian fluid flow and the variable viscosity under shear stress is achieved using a viscosity model known as Cross model.Then,a predictive-corrective method is proposed,by correcting density error with individual stiffness parameters for each particle,to avoid tensile instability and improve numerical stability.Finally,a global adaptive time-stepping method is adopted,which adjusts the time step automatically independent of the scenario and improve efficiency significantly.The results show that the proposed method can model the Newtonian fluid and the shear thinning non-Newtonian fluid,remove the tensile instability,and simulate in larger time step.