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

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Shahvaiz Masood on 18 Sep 2021
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.
close all;
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');
for i=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')
hold on;
% Computing the center of vortex
for i=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)
for j=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
function dxdt=f(x,y)
gamma_val = [-2 2 -2 2];
delta = 0.5;
x0 = [-1 1 -1 1];
y0 = [10 10 -10 -10];
dxdt = 0;
for ii=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
function dydt=g(x,y)
gamma_val = [-2 2 -2 2];
delta = 0.5;
x0 = [-1 1 -1 1];
y0 = [10 10 -10 -10];
dydt = 0;
for ii=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 on 19 Sep 2021
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);
for i = 1:numel(x0)
[t,u1] = ode45(F,[0 1],[x0(i)-1.5 y0(i)+0.3]); % find solution for each initial position
line(u1(:,1),u1(:,2),'color','r')
end
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