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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

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