Report Code inconsistent with the Guide of DeltaSPH

Kyushu_panda

Dear DualSPHysics team,

In DeltaSPH for density correction, the formula in the guide is


While in the code:


So i guess is it the mistake of the guide?

With best Regards.

gfourtakas

Hi Kyushu_panda,

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