3. Numerical Methods |

3.1 Numerical Procedure of the Contour Dynamics Model

3.2 Other Details

3.3 Integral Calculation

## 3.1 Numerical Procedure of the Contour Dynamics Model

< Summary of the theory (section 2.2) >

1.The vorticity distribution is assumed to be

(3.1)

for regions Dj ( j=1,2, ... ,J ) ( Dj1Ç Dj2 = j ) on an infinite plane.

2.The velocity at an arbitrary point on the plane is calculated using the pointsx^{(j)}on each contour C_{j}as

(3.2)

< Procedure to calculate the time evolution of the vorticity distribution >

1.Calculate the velocities of the nodes {x_{i}^{(j)}} on the contours by using (3.2):

(3.3)

2.Integrate (3.3) to know the positions of the contours at the next time t + Δt .

3.Repeat these processes to obtain the time evolution.

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