Particle Simulations in Fluid Dynamics and Molecular Dynamics

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

Krasny 0107187 The investigator develops new computer algorithms for particle simulations in fluid dynamics and molecular dynamics, and he employs the algorithms to study important application problems. The main technical tool is a new adaptive treecode algorithm for solving the N-body problem in the context of long-range particle interactions. In this algorithm, the particle forces or velocities are evaluated using Taylor approximation in Cartesian coordinates, and the necessary Taylor coefficients are computed by a recurrence relation. The adaptive features include a divide-and-conquer evaluation strategy, nonuniform rectangular clusters, variable order approximation, and a run-time choice between Taylor approximation and direct summation. The investigator develops an optimal strategy for choosing the parameters in the code, in order to maximize the accuracy and efficiency of the algorithm. The application problems to be studied in fluid dynamics include the onset of chaotic dynamics in vortex cores, high precision computation of vortex sheet roll-up and spiral formation in the Kelvin-Helmholtz problem, and breakdown and transition in vortex rings. An important component of the work is to compare regularized particle simulations with experiments and with genuine viscous flows computed by finite difference schemes. The application problems to be studied in molecular dynamics involve potential energy and force field evaluation for electrostatic interactions. The results of this research affect several areas of strategic national interest, including civil and military aviation and biotechnology. One outstanding problem in aviation is the simulation of the trailing vortex wake that forms behind an aircraft on takeoff and landing. The vortex wake is a serious hazard to other aircraft, especially in crowded airports. It imposes a minimum time and distance between takeoffs and landings on a given runway, and it is a source of wind shear, which has been implicated in accidents. The project sheds light on the structure and dynamics of vortex cores, and this helps aeronautical engineers in designing vortex wake remediation systems. In the area of biotechnology, one far-reaching problem is to simulate protein folding in a physically accurate way. This is in fact the next step required to make use of the data collected in the human genome project. The project contributes by enhancing the computer algorithms that are used by biochemists to study protein folding. In the area of education and human resources, the investigator directs an applied honors calculus course for freshman science and engineering students, develops a new graduate course on scientific computing, and mentors the professional development of undergraduate and graduate students and postdocs.