Common partial differential equations of computational hydraulics 43
Dt = 1;
Dz = 1;
nm = 19;
im = nm +1;
tm = 5000;
% Initialization of the velocity field;
for m=1:im
u1(m)=0; un1=u1(m);
u2(m)=0; un2=u2(m);
u3(m)=0; un3=u3(m);
end
% Boundary condition at the fixed plate;
u1(im)=0;
u2(im)=0;
u3(im)=0;
% Main program;
for k=1:tm
Dtt=Dt*k;
% Boundary condition at the oscillating plate;
u1(1)= U*sin(2*pi*Dtt/T);
u2(1)= U*sin(2*pi*Dtt/T1);
u3(1)= U*sin(2*pi*Dtt/T);
% Calculation of the horizontal velocities between the
two plates;
for k1=2:nm
0.03
0.02
0.01
–0.01
–0.02
–0.03
–0.04
0
0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Time steps
Shear stress along the oscillating plate (cm/s) 2
tau1: T = 500 s, v = 0.01 cm 2 /s
tau2: T = 1000 s, v = 0.01 cm 2 /s
tau3: T = 500 s, v = 0.1 cm 2 /s
Figure 3.10 Fluid shear stress adjacent to the oscillating plate.