ABSTRACT
Evaluating the above equation leads to 1. Similarly, a 2D area integral in polar coordinates can be written as:∫∫
W (r)rθdrdθ (B.5)
Thus, the standard 2D SPH kernel function can be derived from the integral above, which is:
Wstd(r) = 4
πh2
{ (1− r2h2 )3 0 ≤ r ≤ h 0 otherwise
(B.6)
Similarly, the spiky 3D SPH kernel function is
Wspiky(r) = 15
πh3
{ (1− rh )3 0 ≤ r ≤ h 0 otherwise
(B.7)
— 13:03
— 13:03
Wspiky(r) = 10
πh2
{ (1− rh )3 0 ≤ r ≤ h 0 otherwise
(B.8)
B.2 PCISPH Derivation In a predictive-corrective step from PCISPH, the primary goal is to calculate the correction pressure from the predicted position and the resulting density error. The following derivation is from Solenthaler and Pajarola 2007 [109].
