WEBVTT 00:01.020 --> 00:08.070 Hello and welcome in this particular lecture, this is very interesting lecture here, we will discuss 00:08.100 --> 00:09.960 in depth about meshing. 00:10.320 --> 00:18.650 So a lot of you have asked me why is that important and why in simulation software they use it. 00:18.750 --> 00:24.810 So if you Google and search, it will say that the final dimension, the smaller domain, it will have 00:24.960 --> 00:27.540 and it will have a better solution and so on. 00:27.810 --> 00:30.180 But what does that actually mean? 00:30.390 --> 00:33.540 Let me explain you with a simple example. 00:33.990 --> 00:36.630 Suppose I have a structure. 00:36.750 --> 00:40.550 Let's say I have, uh, cone, OK? 00:41.070 --> 00:42.540 I have some kind of a cone. 00:44.330 --> 00:52.550 And I define this site as tenfold and this as ground. 00:55.340 --> 00:58.140 So basically, this is the zero fault. 00:58.340 --> 01:06.210 OK, so if I zoom in this model, uh, so the cross section will look something like this, right? 01:06.230 --> 01:08.150 It will something be like a triangle. 01:08.840 --> 01:16.220 Now, what they do is that it will divide this region into smaller domains. 01:16.520 --> 01:16.910 Right. 01:16.940 --> 01:18.790 This is what dance does. 01:19.460 --> 01:23.900 And in each smaller domain, it will try to solve. 01:24.960 --> 01:30.980 The solution, so it will take this domain and solve for the solution here and then it will solve here, 01:30.990 --> 01:37.620 it will solve here and so on, and ultimately it will compute the total model. 01:37.920 --> 01:38.200 Right. 01:38.600 --> 01:42.300 But what happens when you take a courser mess? 01:42.780 --> 01:45.170 Suppose Umesh is not fine. 01:45.180 --> 01:48.120 So you have like this. 01:48.690 --> 01:51.090 Maybe it's very coarse. 01:51.120 --> 01:55.650 OK, so what the software will see is that here is one boundary. 01:55.980 --> 01:57.240 Here is another boundary. 01:57.510 --> 01:59.540 Here is one boundary and here is one boundary. 01:59.910 --> 02:02.640 So it will try to solve the solution in this region. 02:03.360 --> 02:06.910 Now take the region, which is present here. 02:07.380 --> 02:09.090 Here you have a sharp edge. 02:10.820 --> 02:17.510 Right, so if you have a coach mess, the software will not be able to differentiate how sharp is the 02:17.510 --> 02:19.470 corner because it is not meshing right. 02:19.790 --> 02:22.530 It is considering the whole region as a single domain. 02:22.940 --> 02:24.110 Do you understand my point? 02:24.500 --> 02:27.150 So hence a finer mesh is needed. 02:27.490 --> 02:30.650 Now, let me explain what will happen when you have a finer mesh. 02:32.150 --> 02:41.060 Let us think that, oh, let me remove this and let's imagine that I zoom in to this stop Dizon. 02:41.120 --> 02:46.580 OK, so the zoomed out version of the tape will look something like this. 02:47.660 --> 02:56.840 Now, if I have a finer mesh, it will have a very fine small domain throughout the geometry and each 02:56.840 --> 03:01.820 domain will be treated like a small area where the equations are right. 03:02.480 --> 03:08.140 So here you can see there, since the smaller boxes are small. 03:08.990 --> 03:17.870 So the solution will be much better because if you see that, suppose you have an image, right? 03:18.710 --> 03:27.710 Let's say you have an image which is one megapixel and you have an image which is 10 megapixel. 03:28.070 --> 03:36.500 So that 10 megapixel image will have a greater resolution than a one megapixel way because the 10 million 03:36.500 --> 03:43.680 pixel image has greater number of dots which contain the information of this image that is similar to 03:43.680 --> 03:46.320 the case in terms of mesh also. 03:46.970 --> 03:48.720 I guess that you get the point. 03:48.950 --> 03:53.560 Now, let me demonstrative a beautiful example which I created myself. 03:54.170 --> 03:59.550 Honestly, I did not get any motivation online through any cause or something. 03:59.810 --> 04:01.310 This idea totally from my own. 04:01.310 --> 04:05.480 Just to explain you all what machine actually does. 04:06.840 --> 04:12.460 So this is a simple model which I made just to show you as an example. 04:12.720 --> 04:16.000 So what I have is this is a sheet of material. 04:16.020 --> 04:18.540 OK, this is a single material. 04:19.410 --> 04:29.880 And it has some connectivity, fine, and this region I have grounded, so this great region is at zero 04:30.120 --> 04:30.520 fault. 04:33.720 --> 04:37.620 This region is at 10 world. 04:39.320 --> 04:45.220 So definitely the current will flow from lower region to the site, right? 04:46.470 --> 04:50.770 And after the simulation, I I'm trying to plot the electric field. 04:51.120 --> 04:52.860 This is my idea. 04:53.250 --> 04:57.180 OK, so the connectivity I took is zero point. 05:00.190 --> 05:07.460 Sorry, zero point one sigma per meter, so this is the connectivity I took for this measure. 05:07.750 --> 05:09.010 So that is not important here. 05:09.200 --> 05:11.120 Oh, the concept is important. 05:11.650 --> 05:14.140 So what is the result we are getting from this? 05:15.400 --> 05:16.130 Let me show you. 05:16.540 --> 05:26.290 So after I have solved the simulation, this is the plot for the electric field in voltage per meter. 05:26.890 --> 05:34.810 So the red region represent the higher electric field and the blue region represent the lower electric 05:34.810 --> 05:35.060 field. 05:35.110 --> 05:39.500 OK, so as you go towards the red reddish region, then it really is high. 05:40.180 --> 05:43.090 So can you spot the problem here? 05:43.630 --> 05:50.440 As you can see, if I show you back and forth from the mesh and the solution, I think you can figure 05:50.440 --> 05:50.830 it out. 05:51.100 --> 05:55.360 If you see here, here I have a box, right? 05:55.850 --> 05:56.770 A single domain. 05:57.460 --> 06:00.490 Now, if you see here, can this party boxier. 06:01.660 --> 06:04.540 So this is the problem, of course. 06:05.270 --> 06:06.200 OK, forget that. 06:06.790 --> 06:08.410 Take this recent. 06:09.400 --> 06:09.810 Right. 06:11.310 --> 06:13.470 Here you can see here's the problem. 06:14.220 --> 06:23.220 So this is one of the reason why you need to use finer mesh, also know that you might think, OK, 06:23.520 --> 06:27.850 this is fine, but we can smooth the result and we can improve it. 06:27.870 --> 06:35.100 So even if you smooth, uh, the plot, there are options in council where you can smooth your result. 06:35.280 --> 06:39.000 So these kind of rough region will be smoothed out. 06:39.480 --> 06:40.430 So after smooth. 06:40.710 --> 06:46.440 Then also the result is not correct because you see there are a lot of sharp regions. 06:47.690 --> 06:51.810 But the electric field is not at all accumulating anywhere. 06:52.230 --> 06:58.760 Also, the electric field is somewhat exploding and this region, which is not correct, right. 06:59.060 --> 07:06.110 Because we know for material electric field gets concentrated near sharp edges whenever current is run 07:06.110 --> 07:06.480 through it. 07:06.920 --> 07:15.540 So there is a lot of inconsistencies, even if you try to, uh, smooth out your solution for your work. 07:16.820 --> 07:18.080 So what can we do? 07:18.350 --> 07:26.260 OK, so here what I've done is I've improved upon our old mesh to this mesh. 07:26.270 --> 07:27.770 So there is a slight improvement. 07:27.770 --> 07:34.130 As you can see, the mesh is quite good after simulating agritourism something like this. 07:34.460 --> 07:37.330 As you can see, it has improved a lot. 07:37.340 --> 07:38.720 If I show you the previous result. 07:38.720 --> 07:44.720 You see, this is the previous result and here's the final result of this mesh. 07:46.360 --> 07:53.860 So still, there are a lot of inconsistencies here because the mesh is not totally smooth, so there 07:53.860 --> 07:59.800 are few regions where the result is not that great, but overall, the result is quite good. 08:00.220 --> 08:04.650 Now here I have a proper machine by proper machine. 08:04.660 --> 08:08.260 I mean, I have a good amount of meshing in the corners. 08:08.560 --> 08:12.550 So you can see in the corners I have a good amount of meshing. 08:13.630 --> 08:16.970 So let's see how the result looks in this case. 08:17.380 --> 08:20.820 So this is the result with proper meshing. 08:20.860 --> 08:27.720 As you can see, the plot looks such a smooth and beautiful and it is consistent also. 08:28.000 --> 08:35.560 So the current is flowing through the lower half to the top and you can see that the court is accommodating 08:35.560 --> 08:38.350 exactly at the corner, which is expected. 08:38.630 --> 08:39.030 Right. 08:39.280 --> 08:46.780 So here the radius of curvature is very small, hence up the electric field is accumulating in this 08:46.780 --> 08:47.240 corner. 08:47.560 --> 08:55.000 So this was a very small example where I wanted to show you the concept of meshing. 08:55.720 --> 09:00.430 And I hope that you liked and learned something from this lecture. 09:01.450 --> 09:02.650 I have a small request. 09:02.650 --> 09:04.390 Please do read my course. 09:04.390 --> 09:08.950 It really helps me to keep my motivation and make more courses. 09:09.110 --> 09:12.070 So thank you for watching and take care.