FINITE-TIME BLOWUP RELATED TO PARTICLE COLLISION IN DIRECT EULERIAN SIMULATION

This study inspired by Falkovich et al. (2002) aims to investigate the motion of particles in turbulence using Eulerian approach under the assumption that particle velocity is a smooth function in space and is uniquely determined by the particle position until collisions between particles occur. When the first collision happens, a discontinuity in the particle velocity gradient appears, resulting in finite-time blowup. Using this approach, the singularities in particle velocity gradient, particle number density, and particle vorticity for various Stokes numbers and gravity factors are investigated numerically in a simple and intuitive Taylor-Green vortex flow, two-dimensional turbulence, and three-dimensional isotropic turbulence.