## 2D Vector Example

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Vec2dex.m % Written by Ebenezer P Gnanamanickam% Dec 2006. % DISCLAIMER - I do not claim to be an expert on MATLAB but what little I % have learned during the course of grad school here at Purdue University % I want to share. If its useful GREAT if not sorry. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This script gives an idea of how to carry out matrix operations in MATLAB % using Blasius boundary layer profile as an example. Here I calculate and % plot the boundary layer profile for various free stream velocities at % different x locations. i.e delta=f(U_inf,x) . % You can choose between three ways of doing it % (i) nested for loop operations with variable declaration/memory % allocation % (ii) single for loop operations - so I use vector operations for one set % of independent variables. % (iii) Complete vector operations - now this is fancy and please NOTE it % uses up a LOT of memory. I wouldn't recommend it but it marginally speeds % up your code . But when the matrix becomes really really large this % becomes extremely useful. The key to doing this, is to understand that the % computer essentially treats every single matrix stacked up as a long % vector. % Again you can check out for your self the various run times. It's again a % good example for plotting stuff. I delibarately made the plotting more fancy than % it needs to be to make it a useful learning example clc; % clears the command window clear all; % clears all the variables close all; % close all exsisting windows tstart=clock; % starts the clock to calculate the run time %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % INPUTS n=100000; % number of points method=3; % choose the method you want to use %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% mu=1.73e-5*10e-5; % in N-s/m^2 rho=1.229; % in kg/m^3 switch (method) case 1 x=zeros(1,n); x=linspace(0,10,n);% in m U_inf=[1 5 10 20 30 40];% in m/s delta=zeros(length(U_inf),length(x)); for (i=1:1:length(U_inf)) for (j=1:1:length(x)) delta(i,j)=3.5*sqrt(mu*x(j)/rho/U_inf(i)); end end smethod='double for loop operations'; case 2 x=zeros(1,n); x=linspace(0,10,n);% in m U_inf=[1 5 10 20 30 40];% in m/s delta=zeros(length(U_inf),length(x)); for (i=1:1:length(U_inf)) delta(i,:)=3.5.*sqrt(mu.*x./rho/U_inf(i)); end smethod='single for loop operations'; case 3 x=zeros(1,n); x=linspace(0,10,n);% in m U_inf=[1 5 10 20 30 40];% in m/s delta=reshape(3.5*sqrt(mu.*repmat(x,1,length(U_inf))/rho./... reshape(repmat(U_inf,length(x),1),1,length(x)*length(U_inf))),... length(x),length(U_inf)); smethod='vector operations'; end figure plot(x,delta) xlabel('x in m') ylabel('\delta_{99} in m'); title('Blasius - Boundary layer thickness on flat plate'); legend('U_\infty = 1','U_\infty = 5','U_\infty = 10',... 'U_\infty = 20','U_\infty = 30','U_\infty = 40',2); grid; tfinish=clock; % end run time runtime=etime(tfinish,tstart); % estimates the runtimes s1=['number of points = ' num2str(n)] s2=['method = ' smethod] s3=['run time = ' num2str(runtime)]