Okay.
This is the final.
The final thing we need to do is to check our solution.
Does it make sense or not?
In numerical, sometimes we can of course calculate everything and having convergence or we get an answer
that doesn't mean we finished or like we like our answer is correct.
So.
It, of course, goes even though any computation we do in general.
So we have to be always careful and in order to be to get the correct answer.
So here now everything we need to compute and or we need to see the result of our for for the computation
here is we're using the you means the final answer the final computation.
And so the last one got updated is this one.
So you scale.
This is X, I didn't put label for x.
Uh, no, actually, the X label here, I put it two times.
Sorry, it's just a little bit not so important, but I don't like the.
Having not correcting.
Oh, sorry.
Let's run it again from the beginning.
So this one we're plotting the U.
Means the current state of the computation.
So here, if we run it again, it will take the U value, which is not going to be this one.
It's going to be after we update the solution.
So it's not the correct thing to maybe use U, but I will just use the other one.
But first, let's look at the answer.
So the answer basically, as we said, the velocity is going in the up direction and in the right direction
in this way and in this way.
So the the this big velocity thing got the direction of the flow.
So it's going this direction and also the it will get diffused.
So we can see the the the value here in the peak is five and as it gets diffused it will reach 1.8.
And this is at the final time.
So here this is for Si the U velocity.
And if we want to see the velocity, we just change this one to v and u solution v u scale become v
and shift enter.
So here is the V.
Now this is of course not a plotting lesson or not a plotting class, but of course there are many ways
to do it and we can actually see a movie for it if we want.
And so the the the thing is, what I want to say is what if you want to see a solution in between?
In order to do that, you just need to put rather u is u f.
And we know we remember.
Think this one like this.
And.
And you equals.
But just take it this way.
But I think we need to reshape it.
You have zero.
I basically everything and J is everything.
And what we need to put.
Is.
Okay, so now we put the u f u f at point zero.
So this is is a set.
That time as you like.
I don't know.
This is basically you start from here, it's zero.
And let's say you want to see the time.
After ten steps.
It is getting diffused.
It's really interesting.
It's getting diffused.
You see at 50, it's getting more diffused.
A 100.
Is getting more diffuse and is going this direction.
200.
Also going this direction.
300.
And then 400.
And 500.
I don't think we have it because we have 499.
Because it's again, it starts from zero to let's say, for like the last one is 420.
So basically, this is the last solution and this is another way.
Just let's keep it like 100, let's say, and we can see it's diffusing.
Or let's say you want to see like the the diffusing thing.
And 20.
This one like it shows maybe 30 looks better.
So we can see how it goes.
It used to have a peak and then it will collapse a little bit.
That's it for the post-processing and.
I hope I explained well and let's let's next classes will be we're going to actually solve these equations,
not necessarily this equation.
We'll use a heat equation which was a little bit simpler to discretize or to, you know, it has lots
of components.
And so we will solve these things with using pens with torch and later we will do that with a library,
the, the in which we can simplify the way we actually do this coding.