Question regarding gradient of pressure term

Asalih3d

Hey guys!

I am hoping you could help me a little bit with the maths here. I am looking at this formula:



And I just want to understand to understand how the expression for the pressure relationship between particle a and b is derived? Is it just some kind over averaging being applied, which I don't understand? (red line)

Secondly, any special reason to why we do not use the relationship which is used at the stress tensor (blue line) for the pressure gradient?

Could someone clarify it for me?

Kind regards, Ahmed

circles

I just came across the same formulation in Shahriari's dissertation(2011) and he referenced 2 papers.

Vila, J. P. (1999). On particle weighted methods and smooth particle hydrodynamics. Mathematical models and methods in applied sciences, 9(02), 161-209.

Colagrossi, A., & Landrini, M. (2003). Numerical simulation of interfacial flows by smoothed particle hydrodynamics. Journal of computational physics, 191(2), 448-475.


Hope those help.

Asalih3d

Thanks @circles will look into them later - nice of you to remember my post while reading it :-)