The δ-SPH formulation in the guide and code are correct. The answer is simple but I appreciate why it might be confusing (also please refer to the articles cited within our guides):

The δ-SPH term is (ρ_b-ρ_a) as in the guide thus, by simplifying with the ρ_b (of the volume term) it becomes (1-ρ_a/ρ_b). This is correct and you have shown that above.

Now look at the first term on the RHS of Eq. 15 on the guide: dρ/dt=-ρdivu + δ_SPH

We choose to write that term as u_ab and not u_ba thus, the sign on the first term of Eq. 15 is positive and not negative and therefore the sign on the δ-SPH should be minus giving you:

## Comments

The δ-SPH formulation in the guide and code are correct.

The answer is simple but I appreciate why it might be confusing (also please refer to the articles cited within our guides):

The δ-SPH term is (ρ_b-ρ_a) as in the guide thus, by simplifying with the ρ_b (of the volume term) it becomes (1-ρ_a/ρ_b). This is correct and you have shown that above.

Now look at the first term on the RHS of Eq. 15 on the guide:

dρ/dt=-ρdivu + δ_SPH

We choose to write that term as u_ab and not u_ba thus, the sign on the first term of Eq. 15 is positive and not negative and therefore the sign on the δ-SPH should be minus giving you:

(ρ_a/ρ_b-1) as it is in the code.

hope this helps.

Regards,

George