  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 classic Riemann problems(CRPs) coupling, which
treats the fluids on both sides of the heating point as two separate Riemann
problems and then couples them. Under the double CRPs frame, the solution is
self-similar, and only three types of solution 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.
