RDSPH:一种适用于一维非连续条件的新SPH方法

A New One-dimensional Smoothed Particle Hydrodynamics Method in Simulating Discontinuous Problem

基于恢复粒子一致性的光滑粒子流体动力学(RSPH)方法,同时借鉴DCSM P方法,在非连续区间上对未知函数分段泰勒展开,并保留零阶项和一阶项,构建了一套适合于模拟一维非连续物理现象的新SPH方法(RDSPH)。比较不同SPH方程近似二次函数的结果,新方法不仅改进了传统SPH方法存在的边界缺陷问题,同时在非连续区域内也能更有效地修复由非连续引起的核近似截断积分和消除粒子不一致性所造成的误差。

For simulating discontinuous physical phenomenon,this paper puts forward a new one-dimensional formula based on restoring particle inconsistency in smoothed particle hydrodynamics （RSPH）. Applying Taylor series expansion, neglecting the second and higher derivatives, and associating with these equations,the new approach deduces a new kernel and particle approximation without kernel esti- mation. In the numerical simulation, the new formulation not only remedies the boundary deficiency problem in the original SPH but also more efficiently repairs the truncated integral in kernel approximation caused by discontinuity and eliminates the errors from particle inconsistency in discontinuous re- gion.