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

Question

Shahvaiz Masood 2021-9-18

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1455939-how-to-plot-streamline-streakline-and-pathlines-without-using-streamline-streamline-odexx-or-simi

回答： darova 2021-9-19

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