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hi i try to run the code with other number of points, the code doesnt not work with other number of points. May i know the reason

Is this FDM or FVM? I am in dilemma where to consider the corner nodes either in top or inlet? If FVM, how to I reconcile learnings from Dr. Sandip Mazumdar?

Very well explained.....Any newbie can easily understand CFD with such interesting video session. Thanks Tanmay for wonderful content🙏

Nice video! Waiting for more

super helpful, thank you

You are an excellent teacher, those lessons are amazing, will you do some C++ applied to CFD in the future? Also i'm really looking forward to the course you do on Peric's book, thanks a lot.

great explanation , thank you!

For higher reynolds numbers like 1000 or 500, what relaxation parameter values shall we choose? How to understand that?

Great initiative

wouldnt loop be starting from 1 to n-2 ?? in last video we discussed this since conduction is central scheme too we cannot calculate the two ends and hence we need to leave those index.

Hello sir, please share your mail I'd or contact no.

Hi sir need your help for my research work. How can i connect to you sir

Sir if the air is also moving with some velocity along with the free jet, how do we initialize?

Thank you so much Sir. Can you please provide the coding for the case of Slip-flow boundary conditions with discritization

Planar geometry or axisymmetric? How do we find teh volume flow rate?

Sir can you please guide.... For a CAE(CFD) engineer , which programming language is good to learn C++ or python.

Very nice Video. Thank so much sir

A fellow CFD Enthusiast from NIT Hamirpur here. Loved your videos, proud NIT-H Junta!

Sir do you have any video for lid driven cavity fvm method in python

import numpy as np import matplotlib.pyplot as plt import math as m # Geometry Defination and constant parameters (SI Units) L = 1 # Length rho = 1 #density k = 0.1 #diffusion coefficient # Mesh N = int(input("Enter number of nodes:"))# number of cells and cell centers dx = L / N # mesh size x = np.linspace(0,L, 2*N + 1) # grid points at cell center and faces x = np.delete(x, range(2,2*N,2)) # only center values # Defining advection strength and diffusion strength u = float(input("Enter flow field value: ")) # value of flow field F = rho * u #advection strength D = k / dx #diffusion strength Pe = F / D #Peclet Number print(Pe) #Boundary Conidtion phi = np.zeros(N+2) phi[0] = 1 phi[N+1] = 0 # Defining Coefficients based on Finite Volume Method coeff = np.zeros((N,N)) # coefficient matrix # Boundary Node First A1 = 0 #aw A2 = (D - (F/2)) #ae A3 = ((2 * D) + F) * phi[0] #Su A4 = -((2 * D) + F) #Sp A5 = A1 + A2 - A4 #ap # Middle Nodes B1 = A2 #ae B2 = (D + (F/2)) #aw B5 = B1 + B2 #ap # Boundary Node Last C1 = B2 #aw C2 = 0 #ae C3 = ((2 * D) - F) * phi[N+1] #su C4 = -((2 * D) - F) #sp C5 = C1 + C2 - C4 for i in range(N): for j in range(N): if i == j == 0: coeff[i,j] = A5 coeff[i,j+1] = -A2 elif i == j == N-1: coeff[i,j] = C5 coeff[i,j-1] = -A2 elif i == j: coeff[i,j] = B5 coeff[i,j+1]= -A2 coeff[i,j-1]= -B2 # Defining constants constant = np.zeros (N) for i in range(N): if i == 0: constant[0] = A3 if i == N-1: constant[N-1] = C3 # solving matrix t = np.linalg.solve(coeff, constant) #inserting the boundary values in the final result t = np.insert(t, 0 , phi[0]) t = np.insert(t,N+1, phi[N+1]) # Analytical Solution phiA = [] for i in x[1:N+1]: b = m.exp((rho*u*i)/k) - 1 c = m.exp((rho*u*L)/k) - 1 a = phi[0] +((b/c) * (phi[N+1]-phi[0])) phiA.append(a) phiA.insert(0,phi[0]) phiA.insert((len(phiA)+1), phi[N+1]) # Plotting the result plt.figure(figsize=(10, 6)) plt.plot(x, t, marker='o', linestyle='-', color='b', label='Numerical Solution') plt.plot(x, phiA, marker='s', linestyle='-', color='g', label='Analytical Solution') plt.xlabel('Distance (m)', fontsize=14) plt.ylabel('phi', fontsize=14) plt.title('Analytical vs Numerical Solution', fontsize=16) plt.grid(True, which='both', linestyle='--', linewidth=0.5) plt.legend() plt.xticks(fontsize=12) plt.yticks(fontsize=12) plt.tight_layout() # Display the plot plt.show() is this a right approach

import numpy as np import matplotlib.pyplot as plt import math as m # Geometry Defination and constant parameters (SI Units) L = 1 # Length rho = 1 #density k = 0.1 #diffusion coefficient # Mesh N = int(input("Enter number of nodes:"))# number of cells and cell centers dx = L / N # mesh size x = np.linspace(0,L, 2*N + 1) # grid points at cell center and faces x = np.delete(x, range(2,2*N,2)) # only center values # Defining advection strength and diffusion strength u = float(input("Enter flow field value: ")) # value of flow field F = rho * u #advection strength D = k / dx #diffusion strength Pe = F / D #Peclet Number print(Pe) #Boundary Conidtion phi = np.zeros(N+2) phi[0] = 1 phi[N+1] = 0 # Defining Coefficients based on Finite Volume Method coeff = np.zeros((N,N)) # coefficient matrix # Boundary Node First A1 = 0 #aw A2 = (D - (F/2)) #ae A3 = ((2 * D) + F) * phi[0] #Su A4 = -((2 * D) + F) #Sp A5 = A1 + A2 - A4 #ap # Middle Nodes B1 = A2 #ae B2 = (D + (F/2)) #aw B5 = B1 + B2 #ap # Boundary Node Last C1 = B2 #aw C2 = 0 #ae C3 = ((2 * D) - F) * phi[N+1] #su C4 = -((2 * D) - F) #sp C5 = C1 + C2 - C4 for i in range(N): for j in range(N): if i == j == 0: coeff[i,j] = A5 coeff[i,j+1] = -A2 elif i == j == N-1: coeff[i,j] = C5 coeff[i,j-1] = -A2 elif i == j: coeff[i,j] = B5 coeff[i,j+1]= -A2 coeff[i,j-1]= -B2 # Defining constants constant = np.zeros (N) for i in range(N): if i == 0: constant[0] = A3 if i == N-1: constant[N-1] = C3 # solving matrix t = np.linalg.solve(coeff, constant) #inserting the boundary values in the final result t = np.insert(t, 0 , phi[0]) t = np.insert(t,N+1, phi[N+1]) # Analytical Solution phiA = [] for i in x[1:N+1]: b = m.exp((rho*u*i)/k) - 1 c = m.exp((rho*u*L)/k) - 1 a = phi[0] +((b/c) * (phi[N+1]-phi[0])) phiA.append(a) phiA.insert(0,phi[0]) phiA.insert((len(phiA)+1), phi[N+1]) # Plotting the result plt.figure(figsize=(10, 6)) plt.plot(x, t, marker='o', linestyle='-', color='b', label='Numerical Solution') plt.plot(x, phiA, marker='s', linestyle='-', color='g', label='Analytical Solution') plt.xlabel('Distance (m)', fontsize=14) plt.ylabel('phi', fontsize=14) plt.title('Analytical vs Numerical Solution', fontsize=16) plt.grid(True, which='both', linestyle='--', linewidth=0.5) plt.legend() plt.xticks(fontsize=12) plt.yticks(fontsize=12) plt.tight_layout() # Display the plot plt.show() is this a right approach?

where is the 'Domain Size" value explained? why is it this value that the y domain is subtracted from? I understand that the y domain must be reversed to properly plot the numpy data on the cartesian plane. However, where does the domain value play into this?

hey there, one more question for you. at 8:30, you show the code, and identify the equation for T_new[i] = (a_E*T[i-1] + a_W*T[i+1]) / a_P. I'm confused because the generalized finite volume discretization formula was given as a_p = a_e * T_e + a_w * T_w. The T_w should be the lower index as the west face is to the left. Edit - looks like it's set back to normal later in the video. thanks and quick feedback!

Question - at about 13:20, you introduce that the thermal conductivity at the east face could be different than the thermal conductivity at the west face. wouldn't that indicate that k was a function of x, and would have to be handled in the integral appropriately?

thanks for these videos! Question about the example at the end. when plugging in a U value above 5, the resulting values grow exceedingly large. Is this due to the difference in gridded values becoming too large to handle using the simple numerical approach applied here? I'm assuming an analytical solution could handle any sized U value.

I modelled a fluid sediment model in a flume with a circular pier at the middle of the flume to observe the scour, but after running simulation for a few minutes, my velocity vector is not moving down ward, it bends around the pierwall which should be but the downward velocity which causes horseshoe vortex is not showing, the vectors will not moving downward after interacting with the pile, what is the reason? Please help me understand

good!

Very clear explanation !

Sir , i have a question please and i will very happy if you anwser ,what is the best in your opinion to use python or ansys for simulation ❤❤

Just a small correction - exact solution should be {(T_b - T_a)*x/L + (q*x/(2*k) )*(L-x) } + T_a

Never thought I would be doing CFD coding with this ease. During the Masters I use to barely pass the CFD course and wasn't really able to understand the course well. But after going through the theoretical concepts by Prof. Suman (IIT Kharagpur) online lectures and now doing the Python coding it seems so easy and fun to learn CFD and implement it. Thanks Tanmay 😇

Sir, I have question, what about gravity when our channel bottom surface is inclined . At that time the gravity will act vertically, while it should act as perpendicular to the surface

also are we taking the assumption that ue=uw and vn=vs. because when we calculate the a_p the coefficient get cancelled out

hello can you explain the code for the QUICK scheme, please?

Can you also include heat transfer with fluid flow, it could be a simple 1D pipe flow with mass, momentum and energy equation, thanks

Nice lecture but flip window of your video and written which not able to write at a time. Thank you🙏

also why are a_p, a_w and a_e defined inside the loop?

is (rho*u) constant i.e is Fe=Fw?

Can you please tell me logic behind starting from 200 and ending at 864 matlab code line number 20

If we solve this 2D problem with matrix based formulation, it’s NOT necessary to have the numerical error , isn’t it ?!

Hi Tanmay, thank you for providing beginner friendly tutorials. It’s much understandable by this way. I can’t thank you enough. I’m grateful to find your channel!

I am quite confused between the difference of conduction, diffusion and convection. I know what conduction and convection and how they differ from each other. but what is diffusion? Is diffusion and conduction same? or are conduction and convection are types of diffusion? what are the difference between these three?

Hey, this might sound dumb. at 3:48, should it not be -A?

bless you Sir <3

I am so glad that you have produced this series of tutorials. One thing that could be improved is keeping the focus of your entries clearly above the controls of the player at the bottom of the view port, e.g. closer to the center of the viewing window. It was very difficult for me to see what you had typed for the central difference because it was obscured by the progress line. Thank you.

I am going to start my first course related to CFD programming with your python course after learning Ansys. I just need a little guidance from you about which software should I learn as I only want to learn one software. Either Matlab or Python. Can you please suggest me one of these which is most commonly used in the industry nowadays and with which I can go for Phd also in future?

Super informative video. At 10:39, the density is incorrect?

Hi Tanmay, I'm following your lectures and just wanted to say Thanks!! :)