svchb
commented
4 months ago Another formulation can also be found here: J. Morris et al., "Modeling Low Reynolds Number Incompressible Flows Using SPH", In: Journal of Computational Physics, Volume 136, Issue 1, 1997, Pages 214-226. doi: doi.org/10.1006/jcph.1997.5776
which is also used here: G. Fourtakas et al., "Local uniform stencil (LUST) boundary condition for arbitrary 3-D boundaries in parallel smoothed particle hydrodynamics (SPH) models", In: Computers & Fluids, 2019. doi: doi.org/10.1016/j.compfluid.2019.06.009
Assuming incompressibility of the fluid, the viscous acceleration simplifies to $$\frac{d\textbf{v}}{dt} = \frac{\eta}{\rho} \nabla^2 \textbf{v}$$
In Price 2012 the second derivative of a vector is given as
where
Why is Adami 2012 discretizing the above viscous acceleration this way:
Is this the same? Where is the factor of 2?