An adaptive multiresolution method for combustion problems: application to flame ball-vortex interaction

In this article, we present numerical simulations of flame ball-vortex interactions using adaptive multiresolution methods. The numerical scheme for the convection-diffusion-reaction equations modelling this problem is based on a finite volume discretization coupled with a discrete multiresolution analysis. The grid in physical space is adapted dynamically to track the evolution of the solution in scale and space. Time integration is done by an explicit Runge-Kutta scheme. In space we use second-order centered schemes. The implementation is based on a graded tree data structure, which improves both CPU and memory performances, as no fine gridding is required in regions where the solution is smooth. To illustrate the features and the efficiency of the method, we compute several flame ball-vortex interactions and study the role played by the fluid flow on the evolution of the flame ball. We observe the roll-up of the flame ball around the vortex into a snail-like structure. We also put into evidence the flammability limit of the flame ball in function of both vortex and radiation intensities.