Applying a Non-Slip Boundary Condition

clc
clear
M=50;
N=50;
u(1,:)=0;
u(M,:)=0;
u(:,1)=0;
u(:,N)=0;
for i=2:M-1;
    for j=2:N-1;
        u(i,j)=rand;
    end
end
for i=1:M;
    for j=1:N;
        muo(i,j)=5.1*10^-6;
    end
end
u
dy=0.1;
tou(1,:)=0;
tou(M,:)=0;
tou(:,1)=0;
tou(:,N)=0;
   
for i=2:M-1;
    for j=2:N-1;
        tou(i,j)=muo(i,j).*(u(i+1,j+1)-u(i,j))/dy;
    end
end
tou(:,:)   
contour(u)
title('Velocity Field')
xlabel('x axis')
ylabel('y axis')
figure(2)
contour(tou)
title('Shear Stress')
xlabel('x axis')
ylabel('y axis')
pause(14)
close all

Applying a Fourth Order Derivative to a Non-Slip Boundary Condition

clc
clear
M=50;
N=50;
u(1:3,:)=0;
u(M-3:M,:)=0;
u(:,1:3)=0;
u(:,N-3:N)=0;

u;

for i=4:M-4;
    for j=4:N-4;
        u(i,j)=rand;
    end
end
for i=1:M;
    for j=1:N;
        muo(i,j)=5.1*10^-6;
    end
end
 u
dy=0.1;
tou(1:3,:)=0;
tou(M-3:M,:)=0;
tou(:,1:3)=0;
tou(:,N-3:N)=0;

for i=4:M-3;
    for j=4:N-3;
        dudy(i,j)=(-u(i+2,j)+8*u(i+1,j)-8*u(i-1,j)+u(i-2,j))/(12*dy);
    end
end
   
for i=4:M-3;
    for j=4:N-3;
        tou(i,j)=muo(i,j).*dudy(i,j);
    end
end

tou(:,:)   
contour(u)
title('Velocity Field')
xlabel('x axis')
ylabel('y axis')
grid on
axis equal
figure(2)
grid on
contour(tou)
title('Shear Stress')
xlabel('x axis')
ylabel('y axis')
pause(100)
close all

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