Reaction-diffusion-convection (R-D-C) problems are governed by wide spectrum of spatio-temporal scales associated with ranges of physical and chemical processes. Such Problems are called multiscale, multiphysics problems. The challenge associated with R-D-C problems is to bridge these scales and processes as seamlessly as possible. For this purpose, we develop a wavelet-based multiscale simulation framework that couples diverse scales and physics.In a first stage we focus on R-D models. We treat the `fine' reaction-scales stochastically, with kinetic Monte Carlo (kMC). The transport via diffusion possesses larger spatio-temporal scales which are bridged to the kMC with the Compound Wavelet Matrix (CWM) formalism. Since R-D-C problems are dynamical we extend the CWM method via the dynamic-coupling of the kMC and diffusion models. The process is approximated by sequential increments, where the CWM on each increment is used as the starting point for the next, providing better exploration of phase-space. The CWM is extended to two-dimensional diffusion with a reactive line-boundary to show that the computational gain and error depends on the scale-overlap and wavelet-filtering. We improve the homogenization by a wavelet-based scheme for the exchange of information between a reactive and diffusive field by passing information along fine to coarse (up-scaling) and coarse to fine (down-scaling) scales by retaining the fine-scale statistics (higher-order moments, correlations). Critical to the success of the scheme is the identification of dominant scales. The efficiency of the scheme is compared to the homogenization and benchmark model with scale-disparity.To incorporate transport by convection, we then couple the Lattice Boltzmann Model (LBM) and kMC operating at diverse scales for flows around reactive block. Such model explores markedly different physics due to strong interplay between these time-scales. `Small' reaction induced temperature variations are considered for multiscale coupling of the reactions with the flow, showing the discrepancies in the evolutions and yield comparing to the conventional model. The same framework is used to study the reactions induced by hydrodynamic bubble collapse which shows the similar features of the kinetics and yield comparing to conventional models.We culminate to some problems that could be solved using the developed framework and preliminary results are presented as "proof of concept."
展开▼
