This project involves modeling and simulation work for coupled non-linear evolution equations describing complex multi-scale multi-physics scenarios. Mathematically, the objects to be computed are partial differential equations (PDEs) (posed on single or two spatial scales) coupled with large systems of deterministic and/or stochastic differential equations (ODEs and SDEs).
The objects to be simulated are fully discretised in the space and time variables. Both the finite element method (FEM) and the finite volume method (FVM) are used to approximate the multiscale PDEs. The interacting particle systems and random walks models we have in mind will be handled via Monte Carlo methods. Getting the correct coupling among scales is the main theoretical challenge. It is worth noting that since an essential part of the model components need to evaluated using intensive Monte Carlo simulations, most of the simulation time/effort will be spent there.
The concrete applications we have in mind include:
a) morphology formation for organic solar cells - out of interacting ternary mixtures with one evaporating component (the interacting particle systems route).
b) morphology formation for organic solar cells - out of interacting ternary mixtures with one evaporating component (the coupled Marra-type PDE systems route).
c) estimating the mean residence time of pedestrian flows walking in dark or through dense smoke (random walk model)
d) estimating the penetration depth of diffusants into rubber foams (random walk model)
SNIC resources will be used to test the robustness with respect to parameters of the mathematical models behind a)-d).