 Welcome back to the lab session. I would suggest you that pay attention here first. You can start working on the lab after the introduction. I will first introduce all the problems, explain you in detail what is the objective of this lab session, the problems, how you have to prepare the report of the lab. From now onwards, all the lab session, both problems as well as the answer sheets are provided in the doc form. So, these are initially it starts with certain set of problems and then there is a separate answer sheet. Now, once you know by this time you know how to run the program in silo. Once you run, you will get certain figures and here the procedure is given how to save the figure. So, this is you have to save in Windows B, BMP image and so this is the common instructions for all the lab sessions. Basically, two grid generation which I have discussed in detail. One is algebraic method, second is elliptic grid generation method. In each problem, first I will start with some physical situation. Although it is purely a geometrical problem, but I have to give you a feel. So, what I did here is that let us suppose you want to generate grid for external flow above a flat horizontal plate. So, in this case how is your domain? Bottom wall of the domain is flat plate and the top wall is open to the boundary. So, in this case what type of grid you would like to generate? You want fine grid near to the bottom wall. Then the second problem I have taken internal flow in horizontal plane channel, where you want fine grid on both the walls, top boundary as well as bottom boundary. External flow above as well as below the flat plate. Then your flat plate will be in the middle of the domain. So, then you have to do clustering at the middle. So, you can see that the height which I had given is 6 and the plate is at 3 and I had also mentioned the plate is of negligible thickness. So, using your given a program using this program. So, you have to generate because when you run the program there are three options which will come. May be I will show it to you. Go here, use this, go to this window. It has domain length. So, what is the domain length in the problem? What is the height? 6. So, now there are three cases whether you want that y is equals to 0 corresponds to the flow above the flat plate. Second case corresponds to plane channel case. Third flow above as well as below. So, if I take 1, then it has beta. Problem there are two values of beta for which you have to run 1.05 and 1.2. Let me take 1.05, number of grid points in the x and y direction. What is given in the problem? 51 in the x direction, y direction you get the results like this. You click on file, go to export to, select from here the first option. Windows BMP image, then save is let us say 1A. This file is saved. Now you come back here and towards the end you have to generate this type of. Actually you are given, I am showing you the solution. I put the figure also. Right now whatever you have you do not have this image. But you have to paste, run the program, create an image and put it here. Note that there is A, B, C, D, E and there is a caption which mentions very clearly what is expected. What is there in the caption? What is A? Mesh obtained using algebraic reason for clustering at bottom. A, B corresponds to clustering at bottom for two different values of bit. Read the caption carefully and paste appropriate image. For each of the problems you are given this type of answer sheet where whatever you have to report results as mesh here then you have to discuss. So for discuss also I had written that you have to write here only. So limit your discussion to this text box only. So this is the answer sheet for the lab session. So like in this case what is the effect of beta on the quality of the grid? By looking into the variation of the grid quality you can talk of. If Reynolds number changes what type of beta you should use? You have to discuss some such points. So the second problem is elliptic. In fact elliptic generation had taken two problems. One on parallel shape, parallel gram shaped domain which I show. And thereafter, so here you have to plot mesh, discuss the quality of grid obtained and then the third problem you have O, C and H type of grid generation which are shown here. What I have done here is basically one grid size given which is little coarser and you can see that this result matches closely with my lecture slide. So this will give you a confidence that this grid which you have drawn is close to what I show in the lecture slide and then you refine it because the quality of the grid is not that good it is little coarser. If you refine it you get much better smoothness in the grid lines. So the first column here, this is O type grid, this is C type grid, this is H type grid on a coarser grid and these are on the finer grids. And then you have to discuss the quality of the grid at the boundary. So this is the procedure you I will repeat again. You open the program in this directory there are total five programs. First one is the library grid, second is for elliptic grid for inclined plate, then O type, C type, H type grid. I would also like to point out that you should not only run the codes and then copy paste the figure but what is expected is that you should try to understand what is in this code. Like how I calculate this is delta xi and this is the coordinate. I will show you. This is the program where L is the length, H is the height and this is the expression to calculate delta xi and delta zeta. And these are you can look into the expressions which are shown you. This expression has been coded. Let us try to understand it. y is equals to H beta plus 1 minus beta minus 1. You can go to the code and see you will see this. This is beta b plus 1 divided by b minus 1 into to the power of 1 minus zeta. If you try go to the slide I know you do not have slide but I am just trying to correlate and show. Later on I will give you slide so you can compare also beta divided 1 divided by beta minus 1 to the power 1 minus zeta. So all such expression you can see here. It has all these options when grid is equals to 1 the expression is this. One grid is equals to 2 which varies the clustering position varies in this case. Note that I would like to point out that in the third case there is not only one parameter. This beta is a parameter for this first two cases but in the third case there is a third parameter. When you want to do clustering at the interior of the domain you not only need beta but there is another parameter which is d. d represents the location at which you want to do clustering. So you want to do clustering at y is equals to 3. So d will be 3 in this case. So all this expression which I am showing in this slide has been just coded into the. This is easy to program but when you look into the elliptic equation it is an iterative method. This is more involved more complicated. So if you look into that program you will see that if you look into the O type grid you can see various terms. If you remember I had shown in my slides actually this program has been written where there is one to one correspondent between the lecture slide and the program. So you can see in my lecture side there are terms like a, b, c. You can see that a is given by this expression, b is given by this expression, c is given by this expression and these are term 1, term 2, term 3, term 4. So you define different terms. So you see these terms and then b is calculated, term c is calculated like this and all those terms later on are substituted into the final expression like numerator denoted term a, term c. There is one to one correspondence between the lecture slide, the final difference, whatever discretization is shown in the lecture slide the same is implemented into this code. As far as I remember this delta dp is delta xi and this dq is delta zeta. There is slight difference in the symbol but otherwise it is you can see dp is l divided by i max minus 1. Let calculate delta xi and delta zeta and dq is this should be h divided by j max minus 1. It is a square so it is okay but in general. So you can see into the code how it is done. So you can get started and fill up this lab sheet. If you have any question feel free to ask. Any question please? Before we get started with the lab I would like to point out this program which we are given xi lab is very much similar to matlab. So you may have questions that why we prefer this software because one of the main reason is that this opens for software and the second thing is that it has its inbuilt graphics. So in CFD very important part is that you want to see finally the numbers which you generate through figures, colorful figures. If you use FORTRAN or C you need to create your own graphics and this is software which is an open source software and it has own graphics. And the second thing is that it is very easy to debug this program. Like term 1 which I have written here if I want to see what is its value I do not have to go back to the program and write printf term 1. What I do here is that I write term 1 here and I get what happens is that inside the program if you use this semicolon that I will show you some of the as far as programming tricks are concerned. If you write let us say x equals to 3 in the program without a semicolon then you can see in the screen. But if you write x equals to 3 with a semicolon then when you run the program you will not be able to see. So if you want to see the print of any term you just remove this semicolon and run it again. So it is easy to debug as far as this program is concerned and it is easy to understand. Basically if you want to know this is based on C programming language and the syntax is common to C. So I think we can get started with the lab. Anyway we will be there to help you out.