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CLC number: U661.1

On-line Access: 2016-02-02

Received: 2015-03-15

Revision Accepted: 2015-09-18

Crosschecked: 2015-12-16

Cited: 1

Clicked: 1917

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Yu Lu

http://orcid.org/0000-0001-7859-2876

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Journal of Zhejiang University SCIENCE A 2016 Vol.17 No.2 P.130-143

http://doi.org/10.1631/jzus.A1500053


A meshless method based on moving least squares for the simulation of free surface flows


Author(s):  Yu Lu, An-kang Hu, Ya-chong Liu, Chao-shuai Han

Affiliation(s):  College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China; more

Corresponding email(s):   luyu90627@126.com

Key Words:  Meshless method, Moving least squares (MLS), Free surface flows, Finite pointset method (FPM), Dam-breaking flows, Solitary wave propagation, Liquid sloshing of tanks


Yu Lu, An-kang Hu, Ya-chong Liu, Chao-shuai Han. A meshless method based on moving least squares for the simulation of free surface flows[J]. Journal of Zhejiang University Science A, 2016, 17(2): 130-143.

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Abstract: 
In this paper, a meshless method based on moving least squares (MLS) is presented to simulate free surface flows. It is a Lagrangian particle scheme wherein the fluid domain is discretized by a finite number of particles or pointset; therefore, this meshless technique is also called the finite pointset method (FPM). FPM is a numerical approach to solving the incompressible Navier–Stokes equations by applying the projection method. The spatial derivatives appearing in the governing equations of fluid flow are obtained using MLS approximants. The pressure Poisson equation with Neumann boundary condition is handled by an iterative scheme known as the stabilized bi-conjugate gradient method. Three types of benchmark numerical tests, namely, dam-breaking flows, solitary wave propagation, and liquid sloshing of tanks, are adopted to test the accuracy and performance of the proposed meshless approach. The results show that the FPM based on MLS is able to simulate complex free surface flows more efficiently and accurately.

The authors propose a finite pointset method (FPM) for the solution of complex three dimensional incompressible free surface flows with large deformations of the computational domain. The solid wall boundary conditions are taken into account via boundary particles, while the free surface boundary condition is imposed as homogeneous Dirichlet boundary on particles that have been identified by an unspecified ad hoc particle-density-based technique. The governing PDE are discretized with a moving-least-squares-based projection method on a moving domain.

一种基于移动最小二乘无网格法的自由面流动数值研究

目的:自由面流动中的大变形、复杂几何边界等问题一直备受工程界的关注。本文基于拉格朗日观点,采用移动最小二乘的无网格技术数值模拟流场,研究溃坝流、孤立波传播及液舱晃荡等复杂变形的自由面流动,验证该方法的准确性与可靠性。
创新点:1. 通过不可压缩Navier-Stokes方程,采用投影法推导出压力与速度之间的关系;2. 借助移动最小二乘法的思想,对压力泊松方程进行离散求解。
方法:1. 通过理论推导,得出不可压缩流动中压力与速度之间的泊松方程式,并采用移动最小二乘法离散求解该偏微分方程;2. 采用数值计算,对自由面流动问题中的三个典型算例进行模拟;3. 将数值计算结果与文献中的试验结果进行比较。
结论:1. 基于移动最小二乘的无网格法能够较准确地模拟自由面流动中的液体迸溅、翻滚、破碎以及入水等强非线性现象,在处理大变形流动问题时体现出较好的灵活性及较强的自由面模拟能力;2. 对比分析数值计算结果与试验现象,得到一致性较好的结果,验证了该无网格法的准确性与可靠性。

关键词:无网格法;移动最小二乘;自由面流动;有限点法;溃坝流;孤立波传播;液舱晃荡

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

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