Explicit calculation for the pressure Poisson equation to simulate incompressible fluid flows in a mesh-free method,International Journal for Numerical Methods in Fluids

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Explicit calculation for the pressure Poisson equation to simulate incompressible fluid flows in a mesh-free method
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-06-09 , DOI: 10.1002/fld.5022
Tibing Xu ₁

Affiliation

In this study, an equation is derived to explicitly solve the pressure Poisson equation (PPE) in the moving particle semiimplicit method. In the derivation, the PPE is discretized by an improved Laplacian model and the incompressible condition is satisfied by establishing a direct relationship between pressure and the known flow information. An improved gradient model is adopted in the method while a repulsive force is used to handle particle clustering. To validate the method, a hydrostatic problem, the impact of two rectangular fluid patches and dam-breaking flows are simulated. The numerical results are compared with analytical solutions and experimental measurements in terms of free surface, pressure, and velocity. Good agreements in the comparisons are achieved, showing that the method can calculate smooth pressure field and accurate pressure and velocity distributions.

中文翻译：

以无网格方法模拟不可压缩流体流动的压力泊松方程的显式计算

在这项研究中，推导了一个方程来明确求解运动粒子半隐式方法中的压力泊松方程 (PPE)。在推导中，PPE通过改进的拉普拉斯模型离散化，通过建立压力和已知流量信息之间的直接关系来满足不可压缩条件。该方法采用改进的梯度模型，同时利用排斥力处理粒子聚类。为了验证该方法，模拟了流体静力学问题、两个矩形流体块的影响和溃坝流。将数值结果与自由表面、压力和速度方面的解析解和实验测量结果进行比较。在比较中达成了良好的协议，

更新日期：2021-06-09

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