New insights into error accumulation due to biased particle distribution in semi-implicit particle methods

• DOI: 10.1016/j.cma.2021.114219
• Publication Date: 2021-10-25T20:14:34Z
• Authors: Guangtao Duan; Takuya Matsunaga; Seiichi Koshizuka; Akira Yamaguchi; Mikio Sakai
• Keywords: 0103 physical sciences; 01 natural sciences

Abstract This study investigates the instability issue at a free surface when the consistent schemes based on variable differences are applied in semi-implicit particle methods. A semi-analytical error-analysis method is proposed to clarify how the incomplete/biased neighbor support triggers error accumulation and instability. Specifically, the discretization models are decomposed into the center-variable components (CVCs) and neighbor-variable components (NVCs). The influence of different components on error accumulation is analyzed theoretically and numerically. Based on the error analysis, new indices are proposed to evaluate the risk of error accumulation due to the biased neighbor support. Then, novel free-surface-detection conditions are proposed from the indices by detecting the particles prone to error accumulation as free surface particles. Numerical examples demonstrated that the proposed conditions detected fewer free-surface particles but produced more stable simulations compared to the existing conditions.