A linearly implicit DG-ALE method for the evaporation of spherical fuel droplets

A novel method for the simulation of fuel droplets evaporating under spherical symmetry conditions is presented. The scheme considers a high-order discontinuous Galerkin method for the space discretization, which is combined with a moving mesh formulation so as to adequately track the droplet surface. A time-step adaptive, third-order, linearly implicit Runge--Kutta scheme is employed for the time discretization, so that it is only necessary to solve a linear system for each Runge--Kutta stage and large CFL numbers can be attained. To the best of the authors' knowledge, this is the first paper on the application of high-order methods to the analysis of evaporating droplets. The method has been applied to the study of n-butanol, ethanol and n-heptane droplets, showing good agreement with the results reported by other authors.