Novel SPH and MPS Laplacian Models Improved by MLS Method for Solving Poisson equations
The smoothed particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) are well-known and efficient mesh-less numerical methods widely used to investigate a wide range of complicated practical engineering problems. Recently, two modified Laplacian models [1, 2] have been proposed by using...
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| Format: | Article |
| Language: | English |
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K. N. Toosi University of Technology
2024-12-01
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| Series: | Numerical Methods in Civil Engineering |
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| Online Access: | https://nmce.kntu.ac.ir/article_210974_5dad177e8362af0527bd2ae38f69e29c.pdf |
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| author | Gholamreza Shobeyri |
| author_facet | Gholamreza Shobeyri |
| author_sort | Gholamreza Shobeyri |
| collection | DOAJ |
| description | The smoothed particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) are well-known and efficient mesh-less numerical methods widely used to investigate a wide range of complicated practical engineering problems. Recently, two modified Laplacian models [1, 2] have been proposed by using different efficient mathematical techniques, and the analogy between SPH and MPS methods. These two models exhibit significantly superior precision in comparison with several existing modified schemes [3-9] but still suffer from lower accuracy near calculation domain boundaries as they work with the conventional weight or interpolation functions. In this paper, the models were reformulated and further improved by replacing the weight functions with well-known moving least squares (MLS) shape functions without requiring dummy calculation nodes beyond boundaries. The proposed Laplacian models in this study could achieve very accurate results compared with the existing models [1, 2] for the solution of four different two-dimensional Poisson equations on irregular node distributions. |
| format | Article |
| id | doaj-art-1a9cbbf556284242b1509d6fd28c8392 |
| institution | Kabale University |
| issn | 2345-4296 2783-3941 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | K. N. Toosi University of Technology |
| record_format | Article |
| series | Numerical Methods in Civil Engineering |
| spelling | doaj-art-1a9cbbf556284242b1509d6fd28c83922025-01-23T08:03:13ZengK. N. Toosi University of TechnologyNumerical Methods in Civil Engineering2345-42962783-39412024-12-0192293910.61186/NMCE.2406.1061210974Novel SPH and MPS Laplacian Models Improved by MLS Method for Solving Poisson equationsGholamreza Shobeyri0Assistant Professor, Faculty of Civil, Water & Environmental Engineering, Shahid Beheshti University, Tehran, IranThe smoothed particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) are well-known and efficient mesh-less numerical methods widely used to investigate a wide range of complicated practical engineering problems. Recently, two modified Laplacian models [1, 2] have been proposed by using different efficient mathematical techniques, and the analogy between SPH and MPS methods. These two models exhibit significantly superior precision in comparison with several existing modified schemes [3-9] but still suffer from lower accuracy near calculation domain boundaries as they work with the conventional weight or interpolation functions. In this paper, the models were reformulated and further improved by replacing the weight functions with well-known moving least squares (MLS) shape functions without requiring dummy calculation nodes beyond boundaries. The proposed Laplacian models in this study could achieve very accurate results compared with the existing models [1, 2] for the solution of four different two-dimensional Poisson equations on irregular node distributions.https://nmce.kntu.ac.ir/article_210974_5dad177e8362af0527bd2ae38f69e29c.pdfmesh-less methodssphmpsimproved laplacian modelsmls shape functions |
| spellingShingle | Gholamreza Shobeyri Novel SPH and MPS Laplacian Models Improved by MLS Method for Solving Poisson equations Numerical Methods in Civil Engineering mesh-less methods sph mps improved laplacian models mls shape functions |
| title | Novel SPH and MPS Laplacian Models Improved by MLS Method for Solving Poisson equations |
| title_full | Novel SPH and MPS Laplacian Models Improved by MLS Method for Solving Poisson equations |
| title_fullStr | Novel SPH and MPS Laplacian Models Improved by MLS Method for Solving Poisson equations |
| title_full_unstemmed | Novel SPH and MPS Laplacian Models Improved by MLS Method for Solving Poisson equations |
| title_short | Novel SPH and MPS Laplacian Models Improved by MLS Method for Solving Poisson equations |
| title_sort | novel sph and mps laplacian models improved by mls method for solving poisson equations |
| topic | mesh-less methods sph mps improved laplacian models mls shape functions |
| url | https://nmce.kntu.ac.ir/article_210974_5dad177e8362af0527bd2ae38f69e29c.pdf |
| work_keys_str_mv | AT gholamrezashobeyri novelsphandmpslaplacianmodelsimprovedbymlsmethodforsolvingpoissonequations |