A p-adaptive high-order mesh-free framework for fluid simulations in complex geometries
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908677023203328 |
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| author | Feng, Ruofeng King, Jack R. C. Lind, Steven J. |
| author_facet | Feng, Ruofeng King, Jack R. C. Lind, Steven J. |
| contents | This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node distributions using linear combinations of anisotropic basis functions, formulated to ensure the exact reproduction of polynomial fields up to the specified p order. A dynamic p-refinement strategy is developed to refine (increase) or de-refine (decrease) the polynomial order used to approximate derivatives at each node. A new refinement indicator for mesh-free methods is proposed, based on local error estimates of the Laplacian operator, and is incorporated into the solution procedure at minimal added computational cost. Based on this error indicator, a refinement criterion is established to locally adjust the polynomial order p for the solution. The proposed adaptive mesh-free scheme is then applied to a range of canonical PDEs, and its potential is demonstrated in two-dimensional simulations of a compressible reacting flow in porous media. For the test cases studied, the proposed method exhibits potential to save up to 50% of computational costs while maintaining the specified level of accuracy. The results confirm that the developed p-adaptive high-order mesh-free method effectively captures highly non-linear regions where high-order approximation is necessary and reduces computational costs compared to the non-adaptive method, preserving high accuracy and solution stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A p-adaptive high-order mesh-free framework for fluid simulations in complex geometries Feng, Ruofeng King, Jack R. C. Lind, Steven J. Numerical Analysis Fluid Dynamics This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node distributions using linear combinations of anisotropic basis functions, formulated to ensure the exact reproduction of polynomial fields up to the specified p order. A dynamic p-refinement strategy is developed to refine (increase) or de-refine (decrease) the polynomial order used to approximate derivatives at each node. A new refinement indicator for mesh-free methods is proposed, based on local error estimates of the Laplacian operator, and is incorporated into the solution procedure at minimal added computational cost. Based on this error indicator, a refinement criterion is established to locally adjust the polynomial order p for the solution. The proposed adaptive mesh-free scheme is then applied to a range of canonical PDEs, and its potential is demonstrated in two-dimensional simulations of a compressible reacting flow in porous media. For the test cases studied, the proposed method exhibits potential to save up to 50% of computational costs while maintaining the specified level of accuracy. The results confirm that the developed p-adaptive high-order mesh-free method effectively captures highly non-linear regions where high-order approximation is necessary and reduces computational costs compared to the non-adaptive method, preserving high accuracy and solution stability. |
| title | A p-adaptive high-order mesh-free framework for fluid simulations in complex geometries |
| topic | Numerical Analysis Fluid Dynamics |
| url | https://arxiv.org/abs/2511.21224 |