How to express a function both time and spatial dimension dependent?

Hi there,

It seems an easy one but I guess it is not that easy. I have a fluid flowing through a vessel. I want to measure its velocity u1 and u2. the vessel coordinetes from the lateral position x=0 to x=1 in time from t=0 to t=3. The code is :

ii=101;
dt=0.1;
t = 0:dt:10;
dx=0.01; %step size
fik=0.4;
for i=1:ii;
x=(i-1)*dx;
H1D=0.1;
H1=0;
A=0;
AD=0.1;
        fikness=fik*sin(pi*x);
        ub1(i)=(c1b-H1D*(x-0.5)+AD/2*(x-0.5)^2)/(H1-0.5*fikness-A*(x-0.5));
        ub2(i)=(c2b+H1D*(x-0.5)-AD/2*(x-0.5)^2)/(1-H1+0.5*fikness+A*(x-0.5));  
end

H1D=H1D+dt*H1DDOT          %------lets say these H1D, H1DDOT, H1 are time dependent functions.
H1=H1+dt*H1
AD=AD+dt*ADDOT;
A=A+dt*AD

Matlab runs the program above but it is not showing time. For example if I want to see in time t=2 what are the velocities u1 and u2 over the whole vessel (from x=0 to x=1)? How can I plot and see the results Thanks in advance

Answer 1

[Amit]

Well, your time is stored in vector t. So lets say you want to plot ub1 versus time, it will be:

plot(t,ub1);

[Amit]

I think there is something wrong in this code too. You are not looping through time actually. I think this code is done to get velocities at t = 0.1 sec. You did not go further.

You have to loop through time as well.

Just a piece of advice: Matlab have good numerical integrators like ode45 which is more stable that simple euler forward integration that you're doing here.

[Meva]

plot (t,ub1) is not what I want since x axes must be x(lateral position) y axes must be ub1 and ub2 at a special time say t=1 or t=2. I mean we want to see the velocities versus x (lateral position) at time 1st second or 2nd second like that. Thanks a lot.

[Amit]

Like I said, you have done your calculation for the first time step only. You need to go through more time loops.