Enabling-Dynamic Simulators: Stability, Bifurcation and Control Computations for Distributed Parameter Systems

摘要

We developed methodologies for the bifurcation detection and stability analysis of microscopic timesteppers (LB-based. lattice gas or Monte Carlo) based on the Recursive Projection Method (RPM). We demonstrated RPM-based 'coarse' (macroscopic) bifurcation and stability computations for systems for which only microscopic evolution rules are available (LB. KMC, Brownian Dynamics -BD-). We were able to perform the coarse bifurcation analysis of KMC models of surface reactions, of LB models of multiphase-bubbly and of reaction diffusion problems, as well as of BD non-Newtonian rheological problems. New micro- Galerkin simulation methods based on Projective Integrators and Telescopic Projective Integrators were implemented. The 'gaptooth' scheme and the 'patch dynamics' schemes were developed and demonstrated. Methods for doing effective bifurcation analysis using timesteppers (thus sidestepping the necessity of deriving homogenized equations) were developed and demonstrated. Furthermore we implemented RPM around a state-of-the-art massively parallel finite-element based code (codename: MPSalsa) at Sandia, as well as a state of the art chemical plant simulation code (gPROMS) which was used in problems of interest to UTRC (fuel cell reactor train modeling). We also developed and demonstrated methods for the computation of self-similar and 'coarsely' self similar solutions, as well as methods for the coarse control of microscopic simulations.