Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames
This paper is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [17]. The paper [17] derives, by means of a three-scale matched asymptotics, starting from the classical thermo-diffusive model with high activation energies, an...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03733114_v183_n2_p173_Lederman |
| Aporte de: |
| id |
todo:paper_03733114_v183_n2_p173_Lederman |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_03733114_v183_n2_p173_Lederman2023-10-03T15:30:15Z Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames Lederman, C. Roquejoffre, J.-M. Wolanski, N. Combustion Half derivatives High activation energies Linear and nonlinear stability This paper is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [17]. The paper [17] derives, by means of a three-scale matched asymptotics, starting from the classical thermo-diffusive model with high activation energies, an integro-differential equation for the flame radius. In the derivation, it is essential for the Lewis Number - i.e. the ratio between thermal and molecular diffusion - to be strictly less than unity. If ε is the inverse of the - reduced activation energy, the idea underlying the construction of [17] is that (i) the time scale of the radius motion is ε-2, and that (ii) at each time step, the solution is ε-close to a steady solution. In this paper, we give a rigorous proof of the validity of this model under the restriction that the Lewis number is close to 1 - independently of the order of magnitude of the activation energy. The method used comprises three steps: (i) a linear stability analysis near a steady - or quasi-steady - solution, which justifies the fact that the relevant time scale is ε-2; (ii) the rigorous construction of an approximate solution; (iii) a nonlinear stability argument. Fil:Lederman, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03733114_v183_n2_p173_Lederman |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Combustion Half derivatives High activation energies Linear and nonlinear stability |
| spellingShingle |
Combustion Half derivatives High activation energies Linear and nonlinear stability Lederman, C. Roquejoffre, J.-M. Wolanski, N. Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| topic_facet |
Combustion Half derivatives High activation energies Linear and nonlinear stability |
| description |
This paper is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [17]. The paper [17] derives, by means of a three-scale matched asymptotics, starting from the classical thermo-diffusive model with high activation energies, an integro-differential equation for the flame radius. In the derivation, it is essential for the Lewis Number - i.e. the ratio between thermal and molecular diffusion - to be strictly less than unity. If ε is the inverse of the - reduced activation energy, the idea underlying the construction of [17] is that (i) the time scale of the radius motion is ε-2, and that (ii) at each time step, the solution is ε-close to a steady solution. In this paper, we give a rigorous proof of the validity of this model under the restriction that the Lewis number is close to 1 - independently of the order of magnitude of the activation energy. The method used comprises three steps: (i) a linear stability analysis near a steady - or quasi-steady - solution, which justifies the fact that the relevant time scale is ε-2; (ii) the rigorous construction of an approximate solution; (iii) a nonlinear stability argument. |
| format |
JOUR |
| author |
Lederman, C. Roquejoffre, J.-M. Wolanski, N. |
| author_facet |
Lederman, C. Roquejoffre, J.-M. Wolanski, N. |
| author_sort |
Lederman, C. |
| title |
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| title_short |
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| title_full |
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| title_fullStr |
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| title_full_unstemmed |
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| title_sort |
mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| url |
http://hdl.handle.net/20.500.12110/paper_03733114_v183_n2_p173_Lederman |
| work_keys_str_mv |
AT ledermanc mathematicaljustificationofanonlinearintegrodifferentialequationforthepropagationofsphericalflames AT roquejoffrejm mathematicaljustificationofanonlinearintegrodifferentialequationforthepropagationofsphericalflames AT wolanskin mathematicaljustificationofanonlinearintegrodifferentialequationforthepropagationofsphericalflames |
| _version_ |
1807319445256798208 |