Modeling and Simulation of fingering pattern formation in a combustion model

Lina Hu (1) , Claude-Michel Brauner (1, 2) , Jie Shen (1, 3) , Gregory I. Sivashinsky (4)

1 School of Mathematical Sciences
2 IMB - Institut de Mathématiques de Bordeaux
3 Department of Mathematics
4 School of Mathematical Sciences

We consider a model of gas-solid combustion with free interface proposed by L. Kagan and G.I. Sivashinsky. Our approach is twofold: (I) we eliminate the front and get to a fully nonlinear system with boundary conditions; (II) we use a fourth-order pseudo-differential equation for the front to achieve asymptotic regimes in rescaled variables. In both cases, we implement a numerical algorithm based on spectral method and represent numerically the evolution of the char. Fingering pattern formation occurs when the planar front is unstable. A series of simulations are presented to demonstrate the evolution of sparse fingers (I) and chaotic fingering (II).

Mots clés: Gas-solid combustion; Smouldering; Free interface; Spectral method; Asymptotics; Fingering; Pattern formation.; Pattern formation

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Lina Hu, Claude-Michel Brauner, Jie Shen, Gregory I. Sivashinsky. Modeling and Simulation of fingering pattern formation in a combustion model. 2013. ⟨hal-00922315v1⟩