Modeling and simulation of a class of nonlinear coupled reaction-diffusion problems for green applications

The present research regards the development of novel numerical methods for the solution of a large class of problems in the field of generalized thermo-diffusion in visco-elasticity and in advection-reaction-diffusion systems in incompressible Brinkman flows. Challenges in these complex physicomathematical problems regard the strong nonlinearities involved, as well as the presence of dynamical behaviours characterized by very different time scales. To deal with these problems efficiently, splitting-operator time integration techniques are explored in order to decouple the dynamics of the various physical phenomena and compared with fully monolithic strategies. The analysis has played a new incisive role to make simulations and predictions in many applicative problems in which a multi-physic approach is needed to capture fully coupled effects. Applications are the simulation of the thermo-rheologically complex behaviour of the relaxation properties of materials with memory, the chemical degradation process due to aging and moisture diffusion in polymers, bioconvection in porous media of oxytactic bacteria and fingering instabilities of exothermic fronts in incompressible viscous fluids.