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Solving 2D Diffusion Equation using MATLAB Lecture 7 ICFDM
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=VKBgC9YndTw
Now, we are writing a 2D code using MATLAB to solve the diffusion equation. Please write in the comments if you have any question. • #CFD #MATLAB #FluidDynamics #FluidMechanics #MechanicalEngineering #CFDusingMATLAB #NavierStokes #Finitedifferencemethod #Finitevolumemethod • • Suggested readings: • 1) Numerical Heat Transfer and Fluid Flow: Excellent book to get a hang of CFD/HT through finite volume methodology. • https://amzn.to/3mEYuSz • PS: The author invented SIMPLE method :) • 2) An Introduction to Computational Fluid Dynamics: The Finite Volume Method: My goto book for advanced understanding of CFD concept and their applications. • https://amzn.to/3ehkQH4 • PS: Excellent discussion on turbulence! • 3) Computational Fluid Dynamics: An Introduction: Nail the finite differences with this book; my first-ever CFD book and that's what I recommend to anyone else as their first CFD read! • https://amzn.to/37ZHD9e • 4) Fluid Mechanics: Revise your fundamentals through this excellently written book by Prof. White. • https://amzn.to/320BuFT • PS: It's not so fundamental, you'll also gain advanced understanding. • 5) MATLAB: An Introduction with Applications: Handy guide to learn MATLAB effortlessly, can't recommend it enough: • https://amzn.to/3oGIrFM • • The script is as follows: • _________________________________________________________________________________________ • clear all • close all • clc • %% Defining the mesh • n_points = 51; • dom_size = 1; • h = dom_size/(n_points - 1); • %% Initialising the problem • y(n_points, n_points) = 0; • y(1,:) = 1; • y_new(n_points, n_points) = 0; • y_new(1,:) = 1; • error_mag = 1; • error_req = 1e-6; • iterations = 0; • %% Calculations • while error_mag (USE THE LARGER THAN SIGN HERE) error_req • for i = 2:(n_points-1) • for j = 2:(n_points-1) • y_new(i,j) = 0.25.*(y_new(i-1,j) + y(i+1,j) + y_new(i,j-1) + y(i,j+1)); • iterations = iterations + 1; • end • end • % Calculation of error magnitude • error_mag = 0; • for i = 2:(n_points-1) • for j = 2:(n_points-1) • error_mag = error_mag + abs(y(i,j) - y_new(i,j)); • end • end • % Assigning new to be old • y = y_new; • end • %% Plotting • x_dom = ((1:n_points)-1).*h; • y_dom = 1-((1:n_points)-1).*h; • [X,Y] = meshgrid(x_dom,y_dom); • contourf(X,Y,y, 12) • colorbar
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