# 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😊

## Comments

Hello

Perhaps look at the thread here, especially the last messages with my answers:

https://forums.dual.sphysics.org/discussion/2173/ddt-fourtakas-hydrostatic-component/p1

Kind regards

Hi,

Thank you so much for the recommendation, it's been a great help! Another confusion I have though is why in equation 17 in figure 1 is RhopZero subtracted?

Best regards

Perhaps a writing mistake. As you see in my derivation "-1" does not appear in the term

Kind regards

I agree with your final message in that discussion. But the code in the penultimate message still subtracts

rhopzeroand the simulation performs well.This is the same as the DualSPHysics code and https://arxiv.org/abs/2110.10076 shows.

So this is different from the first equation in your last message, and that is what confuses me.🤔

Best regards