Solving 2D Poisson-type equations using meshless SPH method
In the present study, 2D Poisson-type equation is solved by a meshless Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The influence of the kernel function, smoothing length and particle discretizations of problem domain on the solutions of Poisson-type equations is investigated. Compared w...
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2019-06-01
|
| Series: | Results in Physics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379718334818 |
| _version_ | 1819207077610913792 |
|---|---|
| author | Shuai Liu Jiao Li Liang Chen Yanjin Guan Cunsheng Zhang Fuzheng Gao Jun Lin |
| author_facet | Shuai Liu Jiao Li Liang Chen Yanjin Guan Cunsheng Zhang Fuzheng Gao Jun Lin |
| author_sort | Shuai Liu |
| collection | DOAJ |
| description | In the present study, 2D Poisson-type equation is solved by a meshless Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The influence of the kernel function, smoothing length and particle discretizations of problem domain on the solutions of Poisson-type equations is investigated. Compared with other kernel functions, the cubic B-spline kernel function shows good capacity to reproduce a complicated function value and its first and second derivatives, when the smoothing length is chosen as 1.1 times the particles’ distance. Several types of Poisson equations are solved by SSPH method, and the numerical results exhibit a very good accuracy when comparing with the analytical solutions. Keywords: Smoothed Particle Hydrodynamics, Poisson equation, Helmholtz, Kernel function |
| first_indexed | 2024-12-23T05:17:46Z |
| format | Article |
| id | doaj.art-9ba86824f72449f994607129122db1b5 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-23T05:17:46Z |
| publishDate | 2019-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-9ba86824f72449f994607129122db1b52022-12-21T17:58:47ZengElsevierResults in Physics2211-37972019-06-0113Solving 2D Poisson-type equations using meshless SPH methodShuai Liu0Jiao Li1Liang Chen2Yanjin Guan3Cunsheng Zhang4Fuzheng Gao5Jun Lin6Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, ChinaKey Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, ChinaKey Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, ChinaKey Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China; Suzhou Institute of Shandong University, Suzhou 215123, ChinaKey Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, ChinaSchool of Mathematics, Shandong University, Jinan 250061, ChinaSuzhou Institute of Shandong University, Suzhou 215123, China; Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China; Corresponding author at: Suzhou Institute of Shandong University, Suzhou 215123, China.In the present study, 2D Poisson-type equation is solved by a meshless Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The influence of the kernel function, smoothing length and particle discretizations of problem domain on the solutions of Poisson-type equations is investigated. Compared with other kernel functions, the cubic B-spline kernel function shows good capacity to reproduce a complicated function value and its first and second derivatives, when the smoothing length is chosen as 1.1 times the particles’ distance. Several types of Poisson equations are solved by SSPH method, and the numerical results exhibit a very good accuracy when comparing with the analytical solutions. Keywords: Smoothed Particle Hydrodynamics, Poisson equation, Helmholtz, Kernel functionhttp://www.sciencedirect.com/science/article/pii/S2211379718334818 |
| spellingShingle | Shuai Liu Jiao Li Liang Chen Yanjin Guan Cunsheng Zhang Fuzheng Gao Jun Lin Solving 2D Poisson-type equations using meshless SPH method Results in Physics |
| title | Solving 2D Poisson-type equations using meshless SPH method |
| title_full | Solving 2D Poisson-type equations using meshless SPH method |
| title_fullStr | Solving 2D Poisson-type equations using meshless SPH method |
| title_full_unstemmed | Solving 2D Poisson-type equations using meshless SPH method |
| title_short | Solving 2D Poisson-type equations using meshless SPH method |
| title_sort | solving 2d poisson type equations using meshless sph method |
| url | http://www.sciencedirect.com/science/article/pii/S2211379718334818 |
| work_keys_str_mv | AT shuailiu solving2dpoissontypeequationsusingmeshlesssphmethod AT jiaoli solving2dpoissontypeequationsusingmeshlesssphmethod AT liangchen solving2dpoissontypeequationsusingmeshlesssphmethod AT yanjinguan solving2dpoissontypeequationsusingmeshlesssphmethod AT cunshengzhang solving2dpoissontypeequationsusingmeshlesssphmethod AT fuzhenggao solving2dpoissontypeequationsusingmeshlesssphmethod AT junlin solving2dpoissontypeequationsusingmeshlesssphmethod |