Modeling the coupling of reaction kinetics and hydrodynamics in a collapsing cavity.

We introduce a model of cavitation based on the multiphase Lattice Boltzmann method (LBM) that allows for coupling between the hydrodynamics of a collapsing cavity and supported solute chemical species. We demonstrate that this model can also be coupled to deterministic or stochastic chemical reactions. In a two-species model of chemical reactions (with a major and a minor species), the major difference observed between the deterministic and stochastic reactions takes the form of random fluctuations in concentration of the minor species. We demonstrate that advection associated with the hydrodynamics of a collapsing cavity leads to highly inhomogeneous concentration of solutes. In turn these inhomogeneities in concentration may lead to significant increase in concentration-dependent reaction rates and can result in a local enhancement in the production of minor species.

Dynamic compound wavelet matrix method for multiphysics and multiscale problems.

The paper presents the dynamic compound wavelet method (dCWM) for modeling the time evolution of multiscale and/or multiphysics systems via an "active" coupling of different simulation methods applied at their characteristic spatial and temporal scales. Key to this "predictive" approach is the dynamic updating of information from the different methods in order to adaptively and accurately capture the temporal behavior of the modeled system with higher efficiency than the (nondynamic) "corrective" compound wavelet matrix method (CWM), upon which the proposed method is based. The system is simulated by a sequence of temporal increments where the CWM solution on each increment is used as the initial conditions for the next. The numerous advantages of the dCWM method such as increased accuracy and computational efficiency in addition to a less-constrained and a significantly better exploration of phase space are demonstrated through an application to a multiscale and multiphysics reaction-diffusion process in a one-dimensional system modeled using stochastic and deterministic methods addressing microscopic and macroscopic scales, respectively.