### Abstract

This chapter is a summary of the work concerning the Navier-Stokes equation derived from the discrete Boltzmann equation. It considers a model of gas whose molecular velocities are restricted to a set of m constant vectors v_{1},v_{m} in IR^{n}. The purpose of this chapter is to study the hydrodynamical equations derived from the discrete Boltzmann equation by applying the Chapman-Enskog method. This chapter shows that the Navier-Stokes equation is transformed into a symmetric system by change of the dependent variable. It is known that the Navier-Stokes equation can be transformed into a coupled system of a symmetric hyperbolic system and a symmetric strongly parabolic system, by changing the dependent variable from w t o u.

Original language | English |
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Pages (from-to) | 15-30 |

Number of pages | 16 |

Journal | North-Holland Mathematics Studies |

Volume | 160 |

Issue number | C |

DOIs | |

Publication status | Published - Jan 1 1989 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*North-Holland Mathematics Studies*,

*160*(C), 15-30. https://doi.org/10.1016/S0304-0208(08)70504-8

**The Navier-Stokes Equation Associated with the Discrete Boltzmann Equation.** / Kawashima, Shuichi; Shizuta, Yasushi.

Research output: Contribution to journal › Article

*North-Holland Mathematics Studies*, vol. 160, no. C, pp. 15-30. https://doi.org/10.1016/S0304-0208(08)70504-8

}

TY - JOUR

T1 - The Navier-Stokes Equation Associated with the Discrete Boltzmann Equation

AU - Kawashima, Shuichi

AU - Shizuta, Yasushi

PY - 1989/1/1

Y1 - 1989/1/1

N2 - This chapter is a summary of the work concerning the Navier-Stokes equation derived from the discrete Boltzmann equation. It considers a model of gas whose molecular velocities are restricted to a set of m constant vectors v1,vm in IRn. The purpose of this chapter is to study the hydrodynamical equations derived from the discrete Boltzmann equation by applying the Chapman-Enskog method. This chapter shows that the Navier-Stokes equation is transformed into a symmetric system by change of the dependent variable. It is known that the Navier-Stokes equation can be transformed into a coupled system of a symmetric hyperbolic system and a symmetric strongly parabolic system, by changing the dependent variable from w t o u.

AB - This chapter is a summary of the work concerning the Navier-Stokes equation derived from the discrete Boltzmann equation. It considers a model of gas whose molecular velocities are restricted to a set of m constant vectors v1,vm in IRn. The purpose of this chapter is to study the hydrodynamical equations derived from the discrete Boltzmann equation by applying the Chapman-Enskog method. This chapter shows that the Navier-Stokes equation is transformed into a symmetric system by change of the dependent variable. It is known that the Navier-Stokes equation can be transformed into a coupled system of a symmetric hyperbolic system and a symmetric strongly parabolic system, by changing the dependent variable from w t o u.

UR - http://www.scopus.com/inward/record.url?scp=77956933294&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956933294&partnerID=8YFLogxK

U2 - 10.1016/S0304-0208(08)70504-8

DO - 10.1016/S0304-0208(08)70504-8

M3 - Article

VL - 160

SP - 15

EP - 30

JO - North-Holland Mathematics Studies

JF - North-Holland Mathematics Studies

SN - 0304-0208

IS - C

ER -