About Density Diffusion Term (Fourtakas et al 2019) in Continuity equation

Hi, I was recently reading the literature on improved δ-sph scheme, but did not understand some of the equations in the text, please see Figure 1:

If the equation of state(EOS) is followed, shouldn't the static density be written in the following form. This is inconsistent with the literature, can anyone point out why?

Another thing that confuses me is why is "RhopZero" subtracted here in the code file of JSphCpu.cpp?

The literature mentioned above is here:

Local uniform stencil (LUST) boundary condition for arbitrary 3-D boundaries in parallel smoothed particle hydrodynamics (SPH) models.https://doi.org/10.1016/j.compfluid.2019.06.009

Best wishes😊


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