Buoyancy driven convection and hysteresis in granular gases: numerical solution

Granular gas-dynamic equations are written down and numerically integrated to study convection. For a two-dimensional gas of inelastic hard disks in a square box and under the effect of gravity, the equations predict buoyancy driven convection triggered by the dynamically created “temperature”-gradient, in coincidence with what has been seen in molecular dynamics simulations and in real 3D experiments. Three states are observed: conductive, one-convective roll and two-convective rolls states. The numerical solution predicts a hysteresis cycle between the last two states.