A Fast Parallel Grid-Free Method for Simulating Turbulent Incompressible Flow In/Around Time-Varying Geometries

Phase I SBIR Project Funded By NSF

This Small Business Innovation Research Phase I project prepares the ground-work for the development of the first commercially available Computational Fluid Dynamics package for a truly grid-free Large Eddy Simulation (LES) of transitional and turbulent incompressible vortex dominated flow in complex time-varying geometries. The computational engine is based on the parallel, fast multipole implementation of a Lagrangian vortex-boundary element method, and turbulence is accounted for via LES, using a Lagrangian dynamic Smagorinsky sub-grid scale model. The method is

  • fully grid-free in the fluid domain,
  • free of numerical diffusion,
  • inherently solution adaptive, and
  • capable of modeling inhomogeneous unsteady wall-bounded turbulent flow.
The salient features of grid-free vortex-based LES modeling of turbulent flows were demonstrated during Phase I using the following prototypical examples.
LES of the self-propagation of a "fat" vortex ring in free space at infinite Reynolds number, initially perturbed by the wave-number of its most unstable bending mode
LES of the head-on collision of two coaxial vortex rings in free space at infinite Reynolds number, initially perturbed by the wave-number of the most unstable bending mode

Wall-bounded turbulent flow examples will be provided during Phase II of the project.

Refer to the Gallery Section for some examples of our first-generation grid-free wall-bounded flow capability.