Riemann problem for constant flow with single-point heating source

Abstract

This work focuses on the Riemann problem of Euler equations with global constant initial conditions and a single-point heating source, which comes from the physical problem of heating one-dimensional inviscid compressible constant flow. In order to deal with the source of Dirac delta-function, we propose an analytical frame of double classical Riemann problems (CRPs) coupling, which treats the fluids on both sides of the heating point as two separate classical Riemann problems and then couples them. Under the double CRPs frame, the Riemann solution is self-similar, and three types of structures are found. The theoretical analysis is also supported by the numerical simulation. Furthermore, the uniqueness of the Riemann solution is established with some restrictions on the Mach number of the initial condition.