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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2016, Vol. 17 Issue (2): 130-143    DOI: 10.1631/jzus.A1500053
Articles     
A meshless method based on moving least squares for the simulation of free surface flows
Yu Lu, An-kang Hu, Ya-chong Liu, Chao-shuai Han
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China; CIMC Ocean Engineering Design & Research Institute Co., Ltd., Shanghai 201206, China
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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.

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     
Received: 15 March 2015      Published: 02 February 2016
CLC:  U661.1  
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Yu Lu
An-kang Hu
Ya-chong Liu
Chao-shuai Han
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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. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2016, 17(2): 130-143.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A1500053     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2016/V17/I2/130

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