Concentration and cavitation of Riemann solutions to two-phase Chaplygin flows under vanishing pressure and flux approximation

Abstract

In this manuscript, the intrinsic phenomena of concentration and cavitation are investigated in the Riemann problem to the pressureless two-phase flow using the three parameters flux approximation. The self-similar solution of the Riemann problem for modified Chaplygin two-phase flows is obtained. It is shown that Riemann solutions for the system under consideration consist two shock wave and one contact discontinuity, which converge to a delta shock wave in the vanishing pressure limit. It is also analyzed that Riemann solution consisting 1-rarefaction wave and 3-rarefaction wave of new approximated model converges to the two contact discontinuities and vacuum state, present between them, for without approximation.