1
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Okay.

2
00:00:01,480 --> 00:00:02,530
This is the final.

3
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The final thing we need to do is to check our solution.

4
00:00:08,420 --> 00:00:09,800
Does it make sense or not?

5
00:00:10,400 --> 00:00:16,820
In numerical, sometimes we can of course calculate everything and having convergence or we get an answer

6
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that doesn't mean we finished or like we like our answer is correct.

7
00:00:23,990 --> 00:00:24,920
So.

8
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It, of course, goes even though any computation we do in general.

9
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So we have to be always careful and in order to be to get the correct answer.

10
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So here now everything we need to compute and or we need to see the result of our for for the computation

11
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here is we're using the you means the final answer the final computation.

12
00:00:56,860 --> 00:01:00,460
And so the last one got updated is this one.

13
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So you scale.

14
00:01:01,930 --> 00:01:05,290
This is X, I didn't put label for x.

15
00:01:06,340 --> 00:01:10,750
Uh, no, actually, the X label here, I put it two times.

16
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Sorry, it's just a little bit not so important, but I don't like the.

17
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Having not correcting.

18
00:01:20,800 --> 00:01:21,330
Oh, sorry.

19
00:01:22,660 --> 00:01:24,970
Let's run it again from the beginning.

20
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So this one we're plotting the U.

21
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Means the current state of the computation.

22
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So here, if we run it again, it will take the U value, which is not going to be this one.

23
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It's going to be after we update the solution.

24
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So it's not the correct thing to maybe use U, but I will just use the other one.

25
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But first, let's look at the answer.

26
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So the answer basically, as we said, the velocity is going in the up direction and in the right direction

27
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in this way and in this way.

28
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So the the this big velocity thing got the direction of the flow.

29
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So it's going this direction and also the it will get diffused.

30
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So we can see the the the value here in the peak is five and as it gets diffused it will reach 1.8.

31
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And this is at the final time.

32
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So here this is for Si the U velocity.

33
00:02:38,690 --> 00:02:47,240
And if we want to see the velocity, we just change this one to v and u solution v u scale become v

34
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and shift enter.

35
00:02:50,030 --> 00:02:51,290
So here is the V.

36
00:02:51,980 --> 00:02:57,500
Now this is of course not a plotting lesson or not a plotting class, but of course there are many ways

37
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to do it and we can actually see a movie for it if we want.

38
00:03:01,550 --> 00:03:09,260
And so the the the thing is, what I want to say is what if you want to see a solution in between?

39
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In order to do that, you just need to put rather u is u f.

40
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And we know we remember.

41
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Think this one like this.

42
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And.

43
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And you equals.

44
00:03:34,050 --> 00:03:36,510
But just take it this way.

45
00:03:39,560 --> 00:03:41,930
But I think we need to reshape it.

46
00:03:46,420 --> 00:03:47,740
You have zero.

47
00:03:47,770 --> 00:03:53,740
I basically everything and J is everything.

48
00:03:56,420 --> 00:03:59,990
And what we need to put.

49
00:04:00,830 --> 00:04:01,580
Is.

50
00:04:07,330 --> 00:04:15,680
Okay, so now we put the u f u f at point zero.

51
00:04:15,700 --> 00:04:18,880
So this is is a set.

52
00:04:20,470 --> 00:04:24,100
That time as you like.

53
00:04:24,490 --> 00:04:25,000
I don't know.

54
00:04:25,720 --> 00:04:29,500
This is basically you start from here, it's zero.

55
00:04:29,740 --> 00:04:33,100
And let's say you want to see the time.

56
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After ten steps.

57
00:04:37,070 --> 00:04:38,780
It is getting diffused.

58
00:04:39,100 --> 00:04:40,360
It's really interesting.

59
00:04:40,370 --> 00:04:42,230
It's getting diffused.

60
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You see at 50, it's getting more diffused.

61
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A 100.

62
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Is getting more diffuse and is going this direction.

63
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200.

64
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Also going this direction.

65
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300.

66
00:05:00,550 --> 00:05:02,560
And then 400.

67
00:05:07,240 --> 00:05:09,150
And 500.

68
00:05:09,160 --> 00:05:14,350
I don't think we have it because we have 499.

69
00:05:15,300 --> 00:05:22,180
Because it's again, it starts from zero to let's say, for like the last one is 420.

70
00:05:22,230 --> 00:05:25,800
So basically, this is the last solution and this is another way.

71
00:05:25,860 --> 00:05:30,270
Just let's keep it like 100, let's say, and we can see it's diffusing.

72
00:05:30,270 --> 00:05:34,740
Or let's say you want to see like the the diffusing thing.

73
00:05:35,530 --> 00:05:37,360
And 20.

74
00:05:38,250 --> 00:05:42,960
This one like it shows maybe 30 looks better.

75
00:05:43,610 --> 00:05:46,700
So we can see how it goes.

76
00:05:46,850 --> 00:05:50,720
It used to have a peak and then it will collapse a little bit.

77
00:05:51,730 --> 00:05:55,510
That's it for the post-processing and.

78
00:05:56,650 --> 00:06:05,650
I hope I explained well and let's let's next classes will be we're going to actually solve these equations,

79
00:06:05,650 --> 00:06:06,880
not necessarily this equation.

80
00:06:06,880 --> 00:06:12,910
We'll use a heat equation which was a little bit simpler to discretize or to, you know, it has lots

81
00:06:12,910 --> 00:06:13,900
of components.

82
00:06:14,080 --> 00:06:26,020
And so we will solve these things with using pens with torch and later we will do that with a library,

83
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the, the in which we can simplify the way we actually do this coding.