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Nonlinear Time-Fractional Differential Equations in Combustion Science

Pagnini, Gianni — 2011

Fractional Calculus and Applied Analysis

MSC 2010: 34A08 (main), 34G20, 80A25 The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar anomalous...

Wildland fire propagation modelling: A novel approach reconciling models based on moving interface methods and on reaction-diffusion equations

Kaur, Inderpreet;  Mentrelli, Andrea;  Bosseur, Frederic;  Filippi, Jean Baptiste;  Pagnini, Gianni — 2015

Application of Mathematics 2015

A novel approach to study the propagation of fronts with random motion is presented. This approach is based on the idea to consider the motion of the front, split into a drifting part and a fluctuating part; the front position is also split correspondingly. In particular, the drifting part can be related to existing methods for moving interfaces, for example, the Eulerian level set method and the Lagrangian discrete event system specification. The fluctuating part is the result of a comprehensive...

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