### Abstract

A simplified asymptotic model has been developed for studying nonlinear detonation waves in chemically reacting fluids which propagate with wave speed close to the acoustical sound speed. In this regime the fluid mechanical and chemical phenomena interact substantially with each other. The model provides simplified equations for describing this interaction. When the model is specialized to unidirectional combustion waves advancing into a region of uniform flow, the travelling waves of this model system moving with positive speed coincide with the travelling waves in a qualitative model for such effects introduced previously by the second author. Some interesting new combustion waves with partial burning are also analyzed. The two main assumptions in deriving the asymptotic model are weak nonlinearity and a sufficiently high activation energy for the chemical kinetics.

Original language | English (US) |
---|---|

Pages (from-to) | 1086-1118 |

Number of pages | 33 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 43 |

Issue number | 5 |

State | Published - Oct 1983 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*43*(5), 1086-1118.

**WEAKLY NONLINEAR DETONATION WAVES.** / Rosales, Rodolfo R.; Majda, Andrew.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 43, no. 5, pp. 1086-1118.

}

TY - JOUR

T1 - WEAKLY NONLINEAR DETONATION WAVES.

AU - Rosales, Rodolfo R.

AU - Majda, Andrew

PY - 1983/10

Y1 - 1983/10

N2 - A simplified asymptotic model has been developed for studying nonlinear detonation waves in chemically reacting fluids which propagate with wave speed close to the acoustical sound speed. In this regime the fluid mechanical and chemical phenomena interact substantially with each other. The model provides simplified equations for describing this interaction. When the model is specialized to unidirectional combustion waves advancing into a region of uniform flow, the travelling waves of this model system moving with positive speed coincide with the travelling waves in a qualitative model for such effects introduced previously by the second author. Some interesting new combustion waves with partial burning are also analyzed. The two main assumptions in deriving the asymptotic model are weak nonlinearity and a sufficiently high activation energy for the chemical kinetics.

AB - A simplified asymptotic model has been developed for studying nonlinear detonation waves in chemically reacting fluids which propagate with wave speed close to the acoustical sound speed. In this regime the fluid mechanical and chemical phenomena interact substantially with each other. The model provides simplified equations for describing this interaction. When the model is specialized to unidirectional combustion waves advancing into a region of uniform flow, the travelling waves of this model system moving with positive speed coincide with the travelling waves in a qualitative model for such effects introduced previously by the second author. Some interesting new combustion waves with partial burning are also analyzed. The two main assumptions in deriving the asymptotic model are weak nonlinearity and a sufficiently high activation energy for the chemical kinetics.

UR - http://www.scopus.com/inward/record.url?scp=0020830109&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020830109&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0020830109

VL - 43

SP - 1086

EP - 1118

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 5

ER -