Formation of a shock wave in a dusty gas by a moving piston

The nonstationary flow induced by a piston moving impulsively at a constant speed in a dusty gas is studied analytically. The effect of suspended particles on a fully developed shock wave is discussed on the basis of an idealized equilibrium-gas approximation. The equations of motion are also solved numerically by means of a modified random-choice method and an operator-splitting technique for the cases when the final shock structure is partially or fully dispersed. The numerical results show the detailed behaviour of the flow in a transitional nonequilibrium state. The case when the particles that collide with the surface of the piston reflect elastically is investigated together with the case when they stick to it. When the particles are reflected from the piston at high speed, they move faster than the shock front for a while. The shock front in this case propagates initially at a larger velocity than in the pure gas case.