Smoothed Particle Hydrodynamics (SPH) is plagued by the phenomenon of tensile instability, which is the occurrence of short wavelength zero energy modes resulting in unphysical clustering of particles. The root cause of the instability is the shape of derivative of the compactly supported kernel function which may yield negative stiffness in the particle interaction under certain circumstances. In this work, an adaptive algorithm is developed to remove tensile instability in SPH for weakly compressible fluids. Herein, a B-spline function is used as the SPH kernel and the knots of the B-spline are adapted to change the shape of the kernel, thereby satisfying the condition associated with stability. The knot-shifting criterion is based on the particle movement within the influence domain. This enables the prevention of instability in fluid problems where excessive rearrangement of particle positions occurs. A 1D dispersion analysis of an Oldroyd B fluid material model is performed to show how the algorithm prevents instabilities for short wavelengths but ensures accuracy at large wavelengths. The efficacy of the approach is demonstrated through a few benchmark fluid dynamics simulations where a visco-elastic Oldroyd B material model and a non-viscous Eulerian fluid material model are considered.

翻译：光滑粒子流体动力学(SPH)深受拉伸不稳定性困扰，该现象指短波长零能模式导致粒子出现非物理性聚集。其根本原因在于紧支核函数导数的形状在特定条件下可能使粒子相互作用产生负刚度。本文开发了一种自适应算法以消除弱可压缩流体SPH中的拉伸不稳定性。该算法采用B样条函数作为SPH核函数，通过自适应调整B样条节点改变核函数形状，从而满足与稳定性相关的条件。节点移动准则基于粒子在影响域内的运动情况，这使得能够预防流体问题中因粒子位置过度重组引发的不稳定性。通过对Oldroyd B流体材料模型进行一维色散分析，展示了该算法如何抑制短波长不稳定性并确保长波长计算精度。通过数个基准流体动力学仿真验证了该方法的有效性，其中分别考虑了粘弹性Oldroyd B材料模型和无粘欧拉流体材料模型。