Particle dynamics simulations of the Navier-Stokes flow with hard disks
Flow simulation with a particle dynamics method is studied. The fluid is made of hard particles which obey the Newtonian equations of motion and the collisions between particles are elastic, that is, energy and momentum are conserved. The viscosity appears autonomously together with the local equilibrium state. When a particle collides with a nonslip boundary, a new velocity is given randomly from the thermal distribution if the wall is isothermal, or a random reflection angle is selected if the wall is adiabatic. Shear viscosity is estimated from simulations of plane Poiseuille flow together with the confirmation that the system obeys the Navier-Stokes equation. Flows past a cylinder are also simulated. Depending on the Reynolds number up to 106, flow patterns are properly reproduced, and Karman vortex shedding is observed. The estimated values of drag coefficient show quantitative agreement with experiments.
particle dynamics simulation hard disk shear viscosity karman vortex drag coefficient