1D and 2D Singular Wavefronts

initialization

dimension

1D

2D

width factor α

1

number of particles N

8

time slice

16

simulation

evolution time

15

animation rate

0.2

stretched view

Yes

No

step 1

process data

step 2

restart

This Demonstration approximates the evolution of the velocity field of 1D and 2D singular wavefronts. The dynamics are fairly well governed by the weak solutions of the Euler–Poincaré differential equation. We use a particle method to solve the equation; all the particles (red points) are initially distributed at random within some area. The data was prepared offline in advance for efficiency. In the 2D case, points have different color opacities according to their individual weights.