The role of the environment in front propagation
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In this work we study the role of a complex environment in the propagation of a front with curvature-dependent speed. The motion of the front is split into a drifting part and a fluctuating part. The drifting part is obtained by using the level set method, and the fluctuating part by a probability density function that gives a comprehensive statistical description of the complexity of the environment. In particular, the environment is assumed to be a diffusive environment characterized by the Erdélyi–Kober fractional diffusion. The evolution of the front is then analysed with a Polynomial Chaos surrogate model in order to perform Sensitivity Analysis on the parameters characterizing the diffusion and Uncertainty Quantification procedures on the modeled interface. Sparse techniques for Polynomial Chaos allowed a limited size for the simulation databases.