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| Numerical solution of the Poisson equation in meshless method based on boundary background grid |
| Received:September 16, 2023 Revised:December 06, 2023 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20230916008 |
| KeyWord:meshless method poisson equation boundary condition virtual particle method background grid |
| Author | Institution |
| 窦立远 |
大连理工大学 船舶工程学院, 大连 |
| 孙哲 |
大连理工大学 船舶工程学院, 大连 |
| 谭思远 |
大连理工大学 船舶工程学院, 大连 |
| 宗智 |
大连理工大学 船舶工程学院, 大连 |
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| Abstract: |
| 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. |
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