Space-time adaptive resolution for reactive flows

Multi-scale systems evolve over a wide range of temporal and spatial scales. The extent of time scales makes both theoretical and numerical analysis difficult, mostly because the time scales of interest are typically much slower than the fastest scales occurring in the system. Systems with such characteristics are usually classified as being stiff. An adaptive mesh refinement method based on the wavelet transform and the G-Scheme framework are used to achieve spatial and temporal adaptive model reduction, respectively, of physical problems described by PDEs. The combination of the methods is proposed to solve PDEs describing reaction-diffusion systems with the minimal number of degrees of freedom, for prescribed accuracies in space and time. Different reaction-diffusion systems are studied with the aim to test the performance and the capability of the combined scheme to generate accurate solutions with respect to reference ones. Several strategies are implemented to improve the performance of the scheme, with minimal loss of accuracy.