Development of new multiscale models for the solution of intermediate regimes in kinetic theory and related fields

Iowa State University, Ames IA

Investigators

Abstract

This project investigates multiscale models that result from the coupling of hydrodynamic equations with kinetic equations in their respective domains of validity. The work, which lies at the interface between functional analysis, physical sciences, scientific computing, and numerical analysis, will develop and analyze algorithms for numerical simulation of coupled Navier-Stokes and Boltzmann-like (Bhatnagar-Gross-Krook (BGK) and Gaussian BGK) equations. Accurate description of many important phenomena in science and engineering relies on models of microscopic behavior of the physical systems. However, computational simulations based on microscopic descriptions are often impossible to realize because of the size of the computational task. Macroscopic models offer a good compromise between physical accuracy and computational efficiency, but such models are often not valid near boundaries and interfaces, or when quantities of interest vary rapidly. In these cases, microscopic effects must be taken into account. This project investigates new multiscale models that consist of physically correct models in different domains of validity, appropriately coupled in regions where more than one model is applicable. This methodology results in a computationally-tractable integro - partial differential system of microscopic and macroscopic equations coupled through their boundary conditions. This project develops the mathematical foundations and computational analysis of these new multiscale models. The results will have implications for simulations of important phenomena in a number of areas, including atmospheric physics, astrophysics, fluid mechanics, plasma physics, and materials science.