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How to plot streamline, streakline and pathlines without using 'streamline streamline, odexx or similar functions in Matlab'

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Shahvaiz Masood
Shahvaiz Masood on 18 Sep 2021
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Answered: darova on 19 Sep 2021
Can someone help me correct my code for tracking centre of vortex and for plotting streamlines, streaklines and pathlines by creating the code and not using Matlab 'streamline' function.
closeall;
clear;
clc;
%3(a)
time_steps = 0.01;
t=0:time_steps:100;
total_time_points=length(t);
load('particle_positions.mat')
figure
plot(xp,yp,'k.')
xlabel('X');
ylabel('Y');
fori=1:length(xp)
[x_val(i),y_val(i)]=Euler_scheme(xp(i),yp(i),total_time_points,time_steps);
end
figure
plot(x_val,y_val,'k.')
xlabel('X');
ylabel('Y');
title('Particle positions')
holdon;
% Computing the center of vortex
fori=1:length(xp)/10 -1
x_center(i) = sum(x_val(i*10:i*10+10))/10;
y_center(i) = sum(y_val(i*10:i*10+10))/10;
end
plot(x_center,y_center,'r*')
xlabel('X');
ylabel('Y');
figure
plot(x_center,y_center,'r*')
xlabel('X');
ylabel('Y');
title('Center of Vortex');
function[x_last,y_last]=Euler_scheme(x,y,l_t,h)
forj=1:l_t-1
x (j + 1) = x (j) + (h * f (x (j), y (j)));
y(j+1)=y(j)+(h*g(x(j),y(j)));
end
x_last=x(end);
y_last=y(end);
end
functiondxdt = f (x, y)
gamma_val = [-2 2 -2 2];
delta = 0.5;
x0 = [-1 1 -1 1];
y0 = [10 10 -10 -10];
dxdt = 0;
forii=1:size(x0,2)
dxdt = dxdt - gamma_val(ii)/(2*pi)*((y-y0(1,ii))/((x-x0(1,ii))^2+(y-y0(1,ii))^2+delta^2));
end
end
functiondydt=g(x,y)
gamma_val = [-2 2 -2 2];
delta = 0.5;
x0 = [-1 1 -1 1];
y0 = [10 10 -10 -10];
dydt = 0;
forii=1:size(x0,2)
dydt = dydt + gamma_val(ii)/(2*pi)*((x-x0(1,ii))/((x-x0(1,ii))^2+(y-y0(1,ii))^2+delta^2));
end
end

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Answers (1)

darova
darova on 19 Sep 2021
Ran in:
What about ode45 ? Streamline is just a trajectory, if you have vector field you can find a solution
[x,y,z] = peaks(20);
[u,v] = gradient(z);
fx = scatteredInterpolant(x(:),y(:),u(:));% function of X velocity
fy = scatteredInterpolant(x(:),y(:),v(:));% function of Y velocity
F = @(t,u) [fx(u(1),u(2)); fy(u(1),u(2))];% ode45 function
quiver(x,y,u,v)
t = 0:.2:2*pi;
(x0, y0) = pol2cart (t)0.5);
fori = 1:numel(x0)
[t,u1] = ode45(F,[0 1],[x0(i)-1.5 y0(i)+0.3]);% find solution for each initial position
行(u1(:,1),u1(:,2),'color','r')
end

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