I'm watching a video on smoothed particle hydrodynamics and this slide:
Claimsit just blindly claims that these smoothing kernels are pretty good.
$$W(r-r_b,h)\equiv\dfrac{315}{64\pi h^9}\left(h^2-|r-r_b|^2\right)^3$$ $$\nabla W(r-r_b,h)\equiv\dfrac{-45}{\pi h^6}\left(h-|r-r_b|\right)^2\left(\dfrac{r-r_b}{|r-r_b|}\right)$$ $$\nabla^2W\equiv\dfrac{45}{\pi h^6}\left(h-|r-r_b|\right)$$
However, it provides no citation, nor does it explain how each of these terms are derived.
Where do these come from?
I'm watching a video on smoothed particle hydrodynamics and this slide:
Claims that these smoothing kernels are pretty good.
However, it provides no citation, nor does it explain how each of these terms are derived.
Where do these come from?
I'm watching a video on smoothed particle hydrodynamics it just blindly claims that these smoothing kernels are pretty good.
$$W(r-r_b,h)\equiv\dfrac{315}{64\pi h^9}\left(h^2-|r-r_b|^2\right)^3$$ $$\nabla W(r-r_b,h)\equiv\dfrac{-45}{\pi h^6}\left(h-|r-r_b|\right)^2\left(\dfrac{r-r_b}{|r-r_b|}\right)$$ $$\nabla^2W\equiv\dfrac{45}{\pi h^6}\left(h-|r-r_b|\right)$$
However, it provides no citation, nor does it explain how each of these terms are derived.
Where do these come from?
