The phenomena of concentration and cavitation in the Riemann solution for the isentropic zero-pressure dusty gasdynamics

The aim of the present paper is to investigate the concentration and cavitation phenomenon in the solution of the Riemann problem (RP) to the pressureless isentropic Euler equations for the dusty gas flow by using the two parameter flux approximation. The similar solution of the RP for dusty gas flow is obtained. The formation of δ-shock and vacuum state in the flow field is discussed. Also, it is shown that the solution, containing two shock waves, of the RP to the isentropic Euler equations for dusty gas converges to the δ-shock wave solution of the transport equations and the solution, containing two rarefaction waves, of the RP converges to the vacuum state solution of the transport equations.