Theory - Anti-symmetry of dWdq

Asalih3dAsalih3d
edited April 2020 in DualSPHysics v4.4

Hello!

My question is regarding this plot basically (from https://shipjournal.co/index.php/sst/article/download/37/142?inline=1);

image.png

As we can see from the blue line, the kernel is symmetric, so wheter a particle is on either side of particle at 0, then the contribution is the same. But for the derivative of the kernel w.r.t. to q, i.e. dWdq (the red line in the plot), it is anti-symmetric, so to me it seems like we have to care about the sign of the contribution.

I have checked a lot of different SPH codes and I can see that many do not do this, i.e. they only care about the absolute size of the contribution and not the direction. Could anyone try to explain to me why, we only care about the absolute value of dWdq and not the sign, even though it is anti-symmetric?

Kind regards

Comments

  • gfourtakasgfourtakas

    Hi,

    We do, dW/dx -> xi-xj/rij dW/drij

    First part is your your vector unit, second part magnitude.

    Regards

    George

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