Despite the many advances in the use of weakly-compressible smoothed particle hydrodynamics (SPH) for the simulation of incompressible fluid flow, it is still challenging to obtain second-order convergence numerically. In this paper we perform a systematic numerical study of convergence and accuracy of kernel-based approximation, discretization operators, and weakly-compressible SPH (WCSPH) schemes. We explore the origins of the errors and issues preventing second-order convergence. Based on the study, we propose several new variations of the basic WCSPH scheme that are all second-order accurate. Additionally, we investigate the linear and angular momentum conservation property of the WCSPH schemes. Our results show that one may construct accurate WCSPH schemes that demonstrate second-order convergence through a judicious choice of kernel, smoothing length, and discretization operators in the discretization of the governing equations.

翻译：尽管在模拟压抑性流体流过程中利用微弱的压抑性流粒体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体体体体体体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流体流