### Abstract

The lattice Boltzmann method (LBM) is the simple numerical simulator for fluids because it consists of linear equations. Excluding the higher differential term, the LBM for a temperature field is also achieved as an easy numerical simulation method. However, the LBM is hardly applied to body fitted coordinates for its formulation. It is then difficult to calculate complex lattices using the LBM. In this paper, the finite element discrete Boltzmann equation (FEDBE) is introduced to deal with this weakness of the LBM. The finite element method is applied to the discrete Boltzmann equation (DBE) of the basic equation of the LBM. For FEDBE, the simulation using complex lattices is achieved, and it will be applicable for the development in engineering fields. The natural convection in a square cavity and the Rayleigh-Bernard convection are chosen as the test problem. Each simulation model is accurate enough for the flow patterns, the temperature distribution and the Nusselt number. This method is now considered good for the flow and temperature field, and is expected to be introduced for complex lattices using the DBE.

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

Pages (from-to) | 113-117 |

Number of pages | 5 |

Journal | Computers and Fluids |

Volume | 40 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2011 Jan |

### Fingerprint

### Keywords

- Discrete Boltzmann equation
- Finite element method
- Thermal lattice Boltzmann method

### ASJC Scopus subject areas

- Computer Science(all)
- Engineering(all)

### Cite this

*Computers and Fluids*,

*40*(1), 113-117. https://doi.org/10.1016/j.compfluid.2010.08.016

**An analysis of natural convection using the thermal finite element discrete Boltzmann equation.** / Seino, Makoto; Tanahashi, Takahiko; Yasuoka, Kenji.

Research output: Contribution to journal › Article

*Computers and Fluids*, vol. 40, no. 1, pp. 113-117. https://doi.org/10.1016/j.compfluid.2010.08.016

}

TY - JOUR

T1 - An analysis of natural convection using the thermal finite element discrete Boltzmann equation

AU - Seino, Makoto

AU - Tanahashi, Takahiko

AU - Yasuoka, Kenji

PY - 2011/1

Y1 - 2011/1

N2 - The lattice Boltzmann method (LBM) is the simple numerical simulator for fluids because it consists of linear equations. Excluding the higher differential term, the LBM for a temperature field is also achieved as an easy numerical simulation method. However, the LBM is hardly applied to body fitted coordinates for its formulation. It is then difficult to calculate complex lattices using the LBM. In this paper, the finite element discrete Boltzmann equation (FEDBE) is introduced to deal with this weakness of the LBM. The finite element method is applied to the discrete Boltzmann equation (DBE) of the basic equation of the LBM. For FEDBE, the simulation using complex lattices is achieved, and it will be applicable for the development in engineering fields. The natural convection in a square cavity and the Rayleigh-Bernard convection are chosen as the test problem. Each simulation model is accurate enough for the flow patterns, the temperature distribution and the Nusselt number. This method is now considered good for the flow and temperature field, and is expected to be introduced for complex lattices using the DBE.

AB - The lattice Boltzmann method (LBM) is the simple numerical simulator for fluids because it consists of linear equations. Excluding the higher differential term, the LBM for a temperature field is also achieved as an easy numerical simulation method. However, the LBM is hardly applied to body fitted coordinates for its formulation. It is then difficult to calculate complex lattices using the LBM. In this paper, the finite element discrete Boltzmann equation (FEDBE) is introduced to deal with this weakness of the LBM. The finite element method is applied to the discrete Boltzmann equation (DBE) of the basic equation of the LBM. For FEDBE, the simulation using complex lattices is achieved, and it will be applicable for the development in engineering fields. The natural convection in a square cavity and the Rayleigh-Bernard convection are chosen as the test problem. Each simulation model is accurate enough for the flow patterns, the temperature distribution and the Nusselt number. This method is now considered good for the flow and temperature field, and is expected to be introduced for complex lattices using the DBE.

KW - Discrete Boltzmann equation

KW - Finite element method

KW - Thermal lattice Boltzmann method

UR - http://www.scopus.com/inward/record.url?scp=78549258083&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78549258083&partnerID=8YFLogxK

U2 - 10.1016/j.compfluid.2010.08.016

DO - 10.1016/j.compfluid.2010.08.016

M3 - Article

AN - SCOPUS:78549258083

VL - 40

SP - 113

EP - 117

JO - Computers and Fluids

JF - Computers and Fluids

SN - 0045-7930

IS - 1

ER -