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Effect of numerical speed of sound and density diffusion on SPH modeling of rigid body migration in plane Poiseuille flow

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Abstract

Migration pattern of a neutrally buoyant object is primarily controlled by the lateral pressure gradient displaying high sensitivity to pressure disturbances in the flow field. Smoothed particle hydrodynamics (SPH) in its standard form is known to exhibit spurious oscillations in the pressure field. A commonly used approach is to introduce numerical diffusion inside the continuity equation for a smoother pressure field creating the popular \(\delta \)-SPH variant. This study focuses on the dependence of lateral pressure gradient evolution on numerical speed of sound and density diffusion for a neutrally buoyant circular cylinder in plane Poiseuille flow. Simulations with and without numerical density diffusion are compared for different numerical speeds of sound in weakly compressible SPH (WCSPH) framework. The \(\delta \)-SPH formulation is observed to display increased pressure oscillations for higher speeds of sound resulting in loss of equilibrium. A scaling correction to the free parameter in \(\delta \)-SPH formulation is proposed. The proposed correction is noted to reduce the pressure oscillations as well as density gradients across the fluid–structure interface significantly, increase overall stability of the scheme and as a result, assist the rigid body to achieve steady motion regardless of the release position.

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The data supporting this study will be made available upon reasonable request for academic use and within the limitations of the provided informed consent by the corresponding author upon acceptance.

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Acknowledgements

The authors would like to acknowledge the reviewers whose insightful comments and suggestions helped us improve and clarify this study.

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  1. Department of Mechanical Engineering, Texas Tech University, Lubbock, 79409, TX, USA

    Doruk Isik & Zhaoming He

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  1. Doruk Isik
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  2. Zhaoming He
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Correspondence to Doruk Isik.

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Isik, D., He, Z. Effect of numerical speed of sound and density diffusion on SPH modeling of rigid body migration in plane Poiseuille flow. Comp. Part. Mech. 10, 503–517 (2023). https://doi.org/10.1007/s40571-022-00511-8

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