Abstract Particle finite element method (PFEM) is a computational tool suitable for simulating fluid dynamics problems characterized by presence of moving boundaries. In this paper a new version of the method for incompressible flow problems is proposed aiming at accuracy improvement. This goal is achieved essentially by applying Strang operator splitting to Navier–Stokes equations and selecting adequate integration schemes for the resulting advective and Stokes sub-problems. For achieving efficient implementation, the pressure and the velocity in the Stokes part are decoupled via the fractional step technique as in the classical PFEM. However, at the first fractional step an explicit pressure prediction procedure for alleviating mass losses is introduced. Three test cases are solved, validating the methodology and estimating its accuracy. The numerical evidence proves that the proposed scheme improves the accuracy of the PFEM.

中文翻译：

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基于Strang分裂的方案提高移动网格粒子有限元法的精度

摘要 粒子有限元法（PFEM）是一种适用于模拟以移动边界为特征的流体动力学问题的计算工具。本文提出了一种新版本的不可压缩流动问题方法，旨在提高精度。这个目标基本上是通过将 Strang 算子分裂应用于 Navier-Stokes 方程并为产生的对流和 Stokes 子问题选择适当的积分方案来实现的。为了实现有效的实施，斯托克斯部分中的压力和速度通过分数阶跃技术与经典 PFEM 中一样解耦。然而，在第一部分步骤中，引入了用于减轻质量损失的显式压力预测程序。解决了三个测试用例，验证了方法并估计了其准确性。