Boundary-velocity error and stability of the accelerated multi-direct-forcing immersed boundary method
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908834975449088 |
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| author | Suzuki, Kosuke Falagkaris, Emmanouil Krüger, Timm Inamuro, Takaji |
| author_facet | Suzuki, Kosuke Falagkaris, Emmanouil Krüger, Timm Inamuro, Takaji |
| contents | The multi-direct-forcing immersed boundary method allows for a small velocity error of the no-slip condition in moving-particle problems but suffers from numerical instability if simulation parameters are not carefully chosen. This study investigates the boundary-velocity error and numerical stability of the accelerated multi-direct-forcing immersed boundary method. An analysis of the discretized equations of body motion in moving boundary problems identifies a critical parameter that solely determines the numerical stability for the body motion. Additionally, numerical simulations reveal the optimal acceleration parameter that minimizes the velocity error of the no-slip condition and is independent of details of the boundary discretisation, the boundary shape, and spatial dimensionality. This study provides a guideline for establishing numerically stable simulations of moving boundary problems at optimal boundary-velocity error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04986 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary-velocity error and stability of the accelerated multi-direct-forcing immersed boundary method Suzuki, Kosuke Falagkaris, Emmanouil Krüger, Timm Inamuro, Takaji Fluid Dynamics Numerical Analysis Computational Physics The multi-direct-forcing immersed boundary method allows for a small velocity error of the no-slip condition in moving-particle problems but suffers from numerical instability if simulation parameters are not carefully chosen. This study investigates the boundary-velocity error and numerical stability of the accelerated multi-direct-forcing immersed boundary method. An analysis of the discretized equations of body motion in moving boundary problems identifies a critical parameter that solely determines the numerical stability for the body motion. Additionally, numerical simulations reveal the optimal acceleration parameter that minimizes the velocity error of the no-slip condition and is independent of details of the boundary discretisation, the boundary shape, and spatial dimensionality. This study provides a guideline for establishing numerically stable simulations of moving boundary problems at optimal boundary-velocity error. |
| title | Boundary-velocity error and stability of the accelerated multi-direct-forcing immersed boundary method |
| topic | Fluid Dynamics Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2507.04986 |