| 窦立远,孙哲,谭思远,宗智.耦合边界背景网格的无网格法泊松方程求解算法[J].计算力学学报,2025,42(2):176~181,220 |
|
| 
码上扫一扫！ |
| 耦合边界背景网格的无网格法泊松方程求解算法 |
| Numerical solution of the Poisson equation in meshless method based on boundary background grid |
| 投稿时间：2023-09-16 修订日期：2023-12-06 |
| DOI：10.7511/jslx20230916008 |
| 中文关键词: 无网格方法 泊松方程 边界条件 虚拟粒子法 背景网格 |
| 英文关键词:meshless method poisson equation boundary condition virtual particle method background grid |
| 基金项目:国家自然科学基金(52171295;52192692);中央高校基本科研业务费(DUT22LK17)资助项目. |
|
| 摘要点击次数: 12 |
| 全文下载次数: 12 |
| 中文摘要: |
| 对于无网格方法而言,常见的边界条件处理方法是在边界外布置虚粒子或镜像粒子。这使得复杂几何边界下粒子排布十分困难,且准确度不高,此外导致基于局部支撑域的插值方法存在支撑域内离散点缺失的问题。而压力Poisson方程的求解需要Neumann或者Dirichlet边界条件,因此如何准确地施加边界条件至关重要。本文提出了一种针对无网格方法中边界条件处理的新方法,通过将原有Poisson方程转化为弱形式的积分方程,可以将边界条件十分方便地直接施加到方程中,避免了边界外增加虚粒子等问题。为了准确计算Poisson方程,在边界附近建立了局部规则背景网格,以规则背景插值点为新的未知变量参与运算,解决了离散点缺失的问题,并保留绝大部分流域的无网格属性。最后通过计算泰勒-格林涡旋问题,验证了所提方法的准确性和可行性。 |
| 英文摘要: |
| For meshless methods,a common approach to handling boundary conditions is to introduce virtual or mirror particles outside the boundary.However,this approach presents challenges in arranging particles accurately for boundaries in complex geometry and can lead to low accuracy.In addition,it results in the issue of missing discrete points within the support domain.The solution of the pressure Poisson equation requires Neumann or Dirichlet boundary conditions,making it crucial to accurately impose boundary conditions.This article proposes a new method for boundary condition handling in meshless methods.By converting the original Poisson equation into a weak-form integral equation,the boundary conditions can be conveniently applied directly to the equation,avoiding issues related to adding virtual particles outside the boundary.To accurately solve the Poisson equation,a local regular background grid is established near the boundary.The regular background interpolation points act as new unknown variables,addressing the problem of missing discrete points and preserving most features of the meshless methods.Finally,the accuracy and feasibility of the proposed method are demonstrated by solving the Taylor- Green vortex problem. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
|
|
|
|
