Modify the Code $3$ given in Kundu et al$.,$ for vorticity$-$stream function formulation of the Navier$-$Stokes equation, such that:

a$)$ The velocity vectors are plotted similar to those in Fig. $6\mathrm{.}15.$

b$)$ The time variation of the vorticity values are plotted at user$-$selected grid points in the mesh on the same graph. Do the same for velocity magnitudes: $V=\sqrt[\phantom{2}]{u^2+v^2}.$

Re$-$run the code for the case shown in Fig. $6\mathrm{.}13$ and submit the modified code and the plots created. Show the modifications made and discuss the results.

Fig. $6-15$