20 dipoles swimming around

20 inviscid doublets advecting themselves around in 2D. The rotation of the doublet axis was obtained by integrating the torque exerted on the doublet solid body (phi=0) only over the side facing the influencing doublet - i.e. the doublet doesn't "see" the backside of other doublets. This is a fudge since the potential flow field is irrotational - and so integrating over the closed contour would produce zero torque. A simple Euler integration scheme was used, and 10,000 passive tracer particles coloured by velocity magnitude were added for effect.

dx(i) / dt = SUM j=1..N, j/=i [k(j) * ((y(j) - y(i)) * cos(q(i)) - (x(j) - x(i)) * sin(q(i))) / ((x(j) - x(i))^2 + (y(j) - y(i))^2)]
dy(i) / dt = SUM j=1..N, j/=i [k(j) * (-(y(j) - y(i)) * sin(q(i)) - (x(j) - x(i)) * cos(q(i))) / ((x(j) - x(i))^2 + (y(j) - y(i))^2)]

Category:

Science & Technology

Tags:

• doublet
• potential
• flow
• inviscid
• dipole
• fluid
• dynamics

[7sorensehn]

huh?