I need help plotting a range of stream lines in my velocity field plot.

I am new to matlab so please excuse my naivety. I need to plot streamlines for psi = [0:1:6] over the range -3<x<3. Any assistance would be greatly appreciated. Here is what I currently have;

[x,y] = meshgrid(-3:.5:3,-3:.5:3); 
u = 2*y; % u velocity function       
v = 1+(2*x); % v velocity function
xmarker = -0.5; %stagnation 'x' point
ymarker = 0; % stagnation 'y' point
figure
hold on 
quiver (x,y,u,v)
plot(xmarker,ymarker,'r*') % stagnation point
axis([-3 3 -3 3]) 

%stream function
psi(0) = y^2 - x^2 - x -0.25

Answer 1

[Ced]

Hi

Nice plotting! I believe contour might help, something like

%stream function
psi = y.^2 - x.^2 - x -0.25;
contour(x,y,psi,[0:1:6])

Cheers

[Jason Harvey]

That worked, thank you very much.

[Ced]

You can "accept" the answer to mark the topic as closed. Thanks!

Answer 2

[Harish babu]

I need help plotting a range of stream lines for velocity and temperature plots in any numerical methods

[Jason Harvey]

HI, I used a quiver plot to provide a velocity field across the plot window and added the contours, as suggested by Ced, and massaged the parameters/resolution to give the result I was looking for. This is the full code I came up with;

clear % clear all stored variables
close all % close all open figures
clc % clear command window

%list variables for velocity field%
[x,y] = meshgrid(-3:.5:3,-3:.5:3); % x and y values for velocity field
u = 2*y; % u velocity function       
v = 1+(2*x); % v velocity function
xmarker = -0.5; %stagnation 'x' point
ymarker = 0; % stagnation 'y' point

%velocity plot%
figure % open a plot window
hold on; box on % hold current figure plot and place box around plot
quiver (x,y,u,v) % plot velocity vector field
plot(xmarker,ymarker,'r*') % stagnation point
axis([-3 3 -3 3]) % fix axis to desired range
title({'Aerodynamics Assignment 1';'Question 1 Velocity and Streamline plots'}) % plot title

%{
%stream function
x2 = [-3:.1:3]; y2 = [-3:.1:3];
psi = y2.^2 - x2.^2 - x2 -0.25; % stream function with constant determined from stagnation point
[C,h] = contour(x,y,psi,[1:1:6]); % plot stream lines from 1 to 6
[B,j] = contour(x,y,psi,[0:1:1],'-.'); % plot zero contour line dashed
clabel(C,h);clabel(B,j); % label contour values
%}

% streamline plots at finer resolution (0.14) to smooth out curves
x2 =[-3:.001:3];

% positive value curve set
psi0 = sqrt(x2.^2 +x2 + 0.25);
psi1 = sqrt(x2.^2 +x2 + 1.25);
psi2 = sqrt(x2.^2 +x2 + 2.25);
psi3 = sqrt(x2.^2 +x2 + 3.25);
psi4 = sqrt(x2.^2 +x2 + 4.25);
psi5 = sqrt(x2.^2 +x2 + 5.25);
psi6 = sqrt(x2.^2 +x2 + 6.25);
plot(x2,psi0,x2,psi1,x2,psi2,x2,psi3,x2,psi4,x2,psi5,x2,psi6)

% negative value curve set
psi00 = -sqrt(x2.^2 +x2 + 0.25);
psi11 = -sqrt(x2.^2 +x2 + 1.25);
psi22 = -sqrt(x2.^2 +x2 + 2.25);
psi33 = -sqrt(x2.^2 +x2 + 3.25);
psi44 = -sqrt(x2.^2 +x2 + 4.25);
psi55 = -sqrt(x2.^2 +x2 + 5.25);
psi66 = -sqrt(x2.^2 +x2 + 6.25);
plot(x2,psi00,x2,psi11,x2,psi22,x2,psi33,x2,psi44,x2,psi55,x2,psi66)

psi_half = sqrt(x2.^2 +x2 + 0.26);
psi0_half = -sqrt(x2.^2 +x2 + 0.26);
plot(x2,psi0_half,x2,psi_half);

Goodluck!

Answer 3

[Kavitha G N]

Need help in plotting the stream lines. I have Orr-sommerfeld equation (1/aR)(D^2 - a^2)^2 Psi - 2i psi - (1-x^2)(D^2 - a^2) psi = c(D^2 - a^2)psi.I have to plot stream lines to this equation with boundaries psi(-1)=0 and psi(1)=0. I have written this but i coldnot validate. Can any one please help to correct this if there are any.

% Define the number of grid points and domain
N = 50;  % Number of grid points
Lx = 10;  % Streamwise domain length
Ly = 2;   % Wall-normal domain length

% Define the x and y vectors based on the grid dimensions
x = linspace(0, Lx, N-1);
y = linspace(0, Ly, N-1);
[X,Y] = meshgrid(x,y);

% Define the Chebyshev differentiation matrix
[D, x] = cheb(N);
D2 = D^2;
D2 = D2(2:N, 2:N);  % Remove boundary points

% Define the Orr-Sommerfeld operators A and B
I = eye(N-1);
a = 0.05;  % Adjust the value of 'a' as needed
R = 500000; % Adjust the value of 'R' as needed

S = diag([0; 1./(1-x(2:N).^2); 0]);
D4 = (diag(1-x.^2)*D^4 - 8*diag(x)*D^3 - 12*D^2)*S;
D4 = D4(2:N, 2:N);

A = (D4 - 2*a^2*D2 + a^4*I) / (a*R) - 2i*I - 1i*diag(1-x(2:N).^2)*(D2 - a^2*I);
B = D2 - a^2*I;

% Calculate eigenvalues and eigenvectors
[vecs, vals] = eig(A, B);

% Find the eigenmode with the maximum growth rate
[max_growth, max_idx] = max(real(diag(vals)));
most_unstable_mode = vecs(:, max_idx);
real_most_unstable_mode =real(most_unstable_mode);
% Reshape the eigenmode to match the grid dimensions
psi = zeros(N-1, N-1);
psi(:, 1:N-1) =reshape(real_most_unstable_mode.*eye(N-1), [], N-1);
disp(psi);
% Create a 2D contour plot of the stream function

contour(X,Y,psi,100,'-b');
xlabel('x');
ylabel('y');

title('Stream Function');