Use stream vorticity equation to solve Lid$-$Driven cavity for Re $=100(129129$ grid$),$ and compare your vorticity filed at x $=0\mathrm{.}5$ and for all $$y$.$

Generate a MATLAB code to solve the following equations simultaneously to generate the Stream function and Vorticity for Lid Driven Cavity Flow based on the following parameters using Jacobi method;

$(^2$ $)/($x$^2)+(^2$ $)/($y$^2)=-$w

$$w$/$t$+$u $$w$/$x$+$v $$w$/$y$=1/$Re $[(^2$ w$)/($x$^2)+(^2$ w$)/($y$^2)]$

u$=$$/$y v$=-$$/$x

Boundary conditions

Left wall; u$=0,$v$=$o

w$(1,$:$)=(-16$$(2,$:$))/($x$^2)-$w$(2,$:$)$

Right wall; u$=0,$v$=$o

w$($N$\_($x$+2),$:$)=(-16$$($N$\_($x$+1),$:$))/($x$^2)-$w$($N$\_($x$+1),$:$)$

Bottom wall; u$=0,$v$=$o

w$($:$,1)=(-16$$($:$,2))/($y$^2)-$w$($:$,2)$

Top wall; u$=1,$v$=$o

w$($:$,$N$\_($y$+2))=(-16$$($:$,$N$\_($y$+1)))/($y$^2)-8/$y$-$w$($:$,$N$\_($y$+1)$