Particle Simulations in Fluid Dynamics and Molecular Dynamics

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Krasny0107187 The investigator develops new computer algorithms forparticle simulations in fluid dynamics and molecular dynamics,and he employs the algorithms to study important applicationproblems. The main technical tool is a new adaptive treecodealgorithm for solving the N-body problem in the context oflong-range particle interactions. In this algorithm, the particleforces or velocities are evaluated using Taylor approximation inCartesian coordinates, and the necessary Taylor coefficients arecomputed by a recurrence relation. The adaptive features includea divide-and-conquer evaluation strategy, nonuniform rectangularclusters, variable order approximation, and a run-time choicebetween Taylor approximation and direct summation. Theinvestigator develops an optimal strategy for choosing theparameters in the code, in order to maximize the accuracy andefficiency of the algorithm. The application problems to bestudied in fluid dynamics include the onset of chaotic dynamicsin vortex cores, high precision computation of vortex sheetroll-up and spiral formation in the Kelvin-Helmholtz problem, andbreakdown and transition in vortex rings. An important componentof the work is to compare regularized particle simulations withexperiments and with genuine viscous flows computed by finitedifference schemes. The application problems to be studied inmolecular dynamics involve potential energy and force fieldevaluation for electrostatic interactions. The results of this research affect several areas ofstrategic national interest, including civil and militaryaviation and biotechnology. One outstanding problem in aviationis the simulation of the trailing vortex wake that forms behindan aircraft on takeoff and landing. The vortex wake is a serioushazard to other aircraft, especially in crowded airports. Itimposes a minimum time and distance between takeoffs and landingson a given runway, and it is a source of wind shear, which hasbeen implicated in accidents. The project sheds light on thestructure and dynamics of vortex cores, and this helpsaeronautical engineers in designing vortex wake remediationsystems. In the area of biotechnology, one far-reaching problemis to simulate protein folding in a physically accurate way. Thisis in fact the next step required to make use of the datacollected in the human genome project. The project contributes byenhancing the computer algorithms that are used by biochemists tostudy protein folding. In the area of education and humanresources, the investigator directs an applied honors calculuscourse for freshman science and engineering students, develops anew graduate course on scientific computing, and mentors theprofessional development of undergraduate and graduate studentsand postdocs.