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arXiv · 2507.04986

Boundary-velocity error and stability of the accelerated multi-direct-forcing immersed boundary method

Kosuke Suzuki·Emmanouil Falagkaris·Timm Krüger·Takaji Inamuro
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Abstract

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.

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Kosuke Suzuki, Emmanouil Falagkaris, Timm Krüger, Takaji Inamuro. 2025-07-07. Boundary-velocity error and stability of the accelerated multi-direct-forcing immersed boundary method. https://arxiv.org/abs/2507.04986

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