Is particle i included in the summation?


I found someone ( writing the momentum equation as:

In this case it does not m atter since ri - ri = 0, and the gradient kernel will produce 0, but in non gradient terms this would matter. Should the summation not include particle i?

Kind regards


  • Hi,

    For most SPH kernels which are symmetric (even) functions (i.e. Wendland kernels) the gradient is zero (odd function) for i-i interaction. For the kernel itself (even) the i-i interaction is has a finite non-zero value and should be included in the summation.

    do a quick check/exercise, use the Wendland kernel with rij=0 and calculate the kernel and its gradient.



  • Hi !

    Thank you very much, it makes sense now!

    Kind regards

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