### Abstract

A direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM) is developed to simulate fluid-particle interaction problems. This method uses the pressure-based LBM to solve the incompressible flow field and the immersed boundary method to handle the fluid-particle interactions. The pressure-based LBM uses the pressure distribution functions instead of the density distribution functions as the independent dynamic variables. The main idea is to explicitly eliminate the compressible effect due to the density fluctuation. In the IB method, a direct-forcing method is introduced to capture the particle motion. It directly computes an IB force density at each lattice grid from the differences between the pressure distribution functions obtained by the LBM and the equilibrium pressure distribution functions computed from the particle velocity. By applying this direct-forcing method, the IB-LBM becomes a purely LBM version. Also, by applying the Gauss theorem, the formulas for computing the force and the torque acting on the particle from the flows are derived from the volume integrals over the particle volume instead of from the surface integrals over the particle surface. The order of accuracy of the IB-LBM is demonstrated on the errors of velocity field, wall stress, and gradients of velocity and pressure. As a demonstration of the efficiency and capabilities of the new method, sedimentation of a large number of spherical particles in an enclosure is simulated.

Original language | English |
---|---|

Pages (from-to) | 648-670 |

Number of pages | 23 |

Journal | International Journal for Numerical Methods in Fluids |

Volume | 66 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2011 Jun 20 |

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### All Science Journal Classification (ASJC) codes

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics

### Cite this

*International Journal for Numerical Methods in Fluids*,

*66*(5), 648-670. https://doi.org/10.1002/fld.2280

}

*International Journal for Numerical Methods in Fluids*, vol. 66, no. 5, pp. 648-670. https://doi.org/10.1002/fld.2280

**A direct-forcing pressure-based lattice Boltzmann method for solving fluid-particle interaction problems.** / Lin, San-Yih; Lin, Chin Tien; Chin, Ya Hsien; Tai, Yuan Hung.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A direct-forcing pressure-based lattice Boltzmann method for solving fluid-particle interaction problems

AU - Lin, San-Yih

AU - Lin, Chin Tien

AU - Chin, Ya Hsien

AU - Tai, Yuan Hung

PY - 2011/6/20

Y1 - 2011/6/20

N2 - A direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM) is developed to simulate fluid-particle interaction problems. This method uses the pressure-based LBM to solve the incompressible flow field and the immersed boundary method to handle the fluid-particle interactions. The pressure-based LBM uses the pressure distribution functions instead of the density distribution functions as the independent dynamic variables. The main idea is to explicitly eliminate the compressible effect due to the density fluctuation. In the IB method, a direct-forcing method is introduced to capture the particle motion. It directly computes an IB force density at each lattice grid from the differences between the pressure distribution functions obtained by the LBM and the equilibrium pressure distribution functions computed from the particle velocity. By applying this direct-forcing method, the IB-LBM becomes a purely LBM version. Also, by applying the Gauss theorem, the formulas for computing the force and the torque acting on the particle from the flows are derived from the volume integrals over the particle volume instead of from the surface integrals over the particle surface. The order of accuracy of the IB-LBM is demonstrated on the errors of velocity field, wall stress, and gradients of velocity and pressure. As a demonstration of the efficiency and capabilities of the new method, sedimentation of a large number of spherical particles in an enclosure is simulated.

AB - A direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM) is developed to simulate fluid-particle interaction problems. This method uses the pressure-based LBM to solve the incompressible flow field and the immersed boundary method to handle the fluid-particle interactions. The pressure-based LBM uses the pressure distribution functions instead of the density distribution functions as the independent dynamic variables. The main idea is to explicitly eliminate the compressible effect due to the density fluctuation. In the IB method, a direct-forcing method is introduced to capture the particle motion. It directly computes an IB force density at each lattice grid from the differences between the pressure distribution functions obtained by the LBM and the equilibrium pressure distribution functions computed from the particle velocity. By applying this direct-forcing method, the IB-LBM becomes a purely LBM version. Also, by applying the Gauss theorem, the formulas for computing the force and the torque acting on the particle from the flows are derived from the volume integrals over the particle volume instead of from the surface integrals over the particle surface. The order of accuracy of the IB-LBM is demonstrated on the errors of velocity field, wall stress, and gradients of velocity and pressure. As a demonstration of the efficiency and capabilities of the new method, sedimentation of a large number of spherical particles in an enclosure is simulated.

UR - http://www.scopus.com/inward/record.url?scp=79955747741&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955747741&partnerID=8YFLogxK

U2 - 10.1002/fld.2280

DO - 10.1002/fld.2280

M3 - Article

VL - 66

SP - 648

EP - 670

JO - International Journal for Numerical Methods in Fluids

JF - International Journal for Numerical Methods in Fluids

SN - 0271-2091

IS - 5

ER -