A Vortex Method for Viscous Flow
This project will develop a novel vortex method for computer simulation of viscous fluid flow described by the Navier-Stokes equations. Applications of interest include flows past solid bodies as they arise in fields such as aerodynamics and bio-locomotion. A key goal is to develop an improved method for computing boundary layer separation. The numerical method will employ (1) a Lagrangian particle/panel representation of the flow map, (2) recently developed techniques for adaptive panel refinement and particle remeshing, (3) a treecode algorithm to reduce the operation count from O(N^2) to O(NlogN), where N is the number of particles in the simulation, and (4) an integral equation approach to treating viscous diffusion and the no-slip condition. Comparisons will be performed with exisiting finite-difference methods to assess the new method's accuracy and efficiency.
Published in the 24th International Congress of Theoretical and Applied Mechanics, 2017
Published in the Physics of Fluids
Presented at the Korea Institute for Advanced Study (KIAS), Seoul, South Korea, December, 2017
Presented at the Annual Meeting, American Physical Society, Division of Fluid Dynamics, Gallery of Fluid Motion, November 2017
$ 75,000 from the Michigan Institute for Computational Discovery and Engineering.
Presented at Joint Mathematics Meetings, Atlanta, Georgia, January 4-7, 2017.
Published in Elsevier.
Presented at the SIAM Annual Meeting, Pittsburgh, Pennsylvania, July 11, 2017.
Presented at the Annual Meeting, American Physical Society, Division of Fluid Dynamics, Portland, Oregon, November 20-22, 2016.