- **Main CFD Forum**
(*https://www.cfd-online.com/Forums/main/*)

- - **Derivation of Gradient in SPH**
(*https://www.cfd-online.com/Forums/main/106515-derivation-gradient-sph.html*)

Dear Scott KulpIt came from a little astute trick, I advise you to read page 43 and 44 of the book "Smoothed particle hydrodynamic particle a meshfree particle method" by G.R.Liu and M.B Liu in order to understand what happened. |

This book is really nice and very informative. I see that equation 2.22 is basically the same as I wrote above (though 2.22 is the divergence), with the negative, and I do understand that. However, in the summary on page 44, equation 2.25 is not negative. I don't see any explanation on why the negative was removed... Any thoughts?
Thanks! |

I understood your question first time,however I think the answer is in page 44 where the authors wrote : "it should be noted that grad(i)Wij is taken with respect to particle i so the negative sign in equation (2.21) is removed in equation (2.25)."
I agree with you there is an vagueness in the notation formulas,maybe we can say the mistake, but the concept is true, W is an even function so grad(W) is an odd one it means W in the equation 2.25 is the symmetry as W in equation 2.22 because the first is about all neighbors(which detected by j counters) and second is about the determined particle itself (i), maybe if you put Wji instead of Wij in eq 2.22 everything become correct. |

All times are GMT -4. The time now is 16:26. |