Numerical investigation of finite-time blowup related to particle collision

This study inspired by Falkovich et al. (2002) aims at numerical investigation of finite-time blowup by collision using a new approach. we have adopted Eulerian framework under the assumption that particle velocity is a smooth function in space and is uniquely determined by the particle position until collision between particles occur. In particular, the particle velocity gradient can easily go to blow up within a finite time due to the discontinuity when the first collision happens. Using this approach, the singularities in particle velocity gradient, particle number density, and particle vorticity for numerous Stokes numbers and gravity factors are investigated allowing a rigorous mathematical description of particle collision. Three background flows such as a simple and intuitive two-dimensional Taylor-Green vortex flow, two-dimensional decaying turbulence, and three-dimensional isotropic turbulence are used for direct Eulerian simulation. In addition, we have revealed a flow condition leading to collision of particles wherein very thin shear layer constructed by two parallel same-signed vortical structures. Detailed results will be presented in the meeting.