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 even for simple periodic domains. 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 despite having a periodic domain. 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使用微弱的压抑性流粒体流体动力学(SPH)取得了许多进展,但即使是在简单的周期性领域,仍难以获得二级趋同,在本文件中,我们对内核近似、离散操作员和微弱压缩性流体动力学(WCSPH)的趋同和准确性进行系统的数字研究。我们探讨了错误的起源和妨碍二级趋同的问题,尽管有一个定期域。根据这项研究,我们提出了基本WCSPH计划的若干新的变异,这些变异都是第二级准确的。此外,我们调查了WCSPH计划线性和角动力保护特性。我们的结果显示,通过明智地选择内核、平滑长和离分解式操作员,可以建立精确的WCSPHPH计划,表明二级趋同。