Riemann problem for a compressible perfect fluid with a constant external force for the Chaplygin gas

Abstract

Abstract The Riemann problem for a compressible perfect fluid with a constant external force for the Chaplygin gas is considered. We obtain two kinds of exact solutions. The first one consists of contact discontinuities, while the other one involves a delta shock wave in which both density and internal energy contain a Dirac delta function. The position, speed and weights of the delta shock wave are derived from both generalized Rankine–Hugoniot relation and entropy condition, which are established in detail. Moreover, the solutions are no longer self-similar due to the influence of the constant external force.

Keywords

• Delta shock wave
• Compressible fluids
• Riemann problem
• Source term