How do I plot Streamlines of velocity components of spherical coordinate system?

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Jagadeesh Korukonda 2022-12-13

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https://ww2.mathworks.cn/matlabcentral/answers/1877222-how-do-i-plot-streamlines-of-velocity-components-of-spherical-coordinate-system

评论： Jagadeesh Korukonda 2022-12-15

采纳的回答： VBBV

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I solved Navier stokes in Spherical coordinates and I got velocity field inside a sphere i.e

If I plot contours using the code below its working. But, The same technique is not working for streamlines, instead I'm getting blank.

The streamlines are look like this

nr = 21;

nth = 21;

L = 1;

r = linspace(0,1,nr);

th = linspace(0,pi,nth);

[R,Th] = meshgrid(r,th);

Xi = R.*cos(Th); Yi = R.*sin(Th);

ui = (R.^2-1)/2/(L+1).*cos(Th);

vi = (1-2*R.^2)/2/(L+1).*sin(Th);

figure;contourf(Xi,Yi,ui,100,'LineStyle','none');axis image

figure;contourf(Xi,Yi,vi,100,'LineStyle','none');axis image

figure;streamline(Xi,Yi,ui,vi)

I'm getting streamlines as empty, can anyone help me in this regard?

Thanks in advance.

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采纳的回答

VBBV 2022-12-13

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1877222-how-do-i-plot-streamlines-of-velocity-components-of-spherical-coordinate-system#answer_1126967

在 MATLAB Online 中打开

verts = stream2(Xi,Yi,ui,vi,R,Th);
streamline(verts);

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VBBV 2022-12-15

在 MATLAB Online 中打开

Ok, it seems your equations are in spherical coordinates, so use sph2cart function

clc

clear all

close all

nr = 21;

nth = 21;

L = 1;

r =linspace(-1,1,nr);

th =linspace(0,pi,nth);

[R,Th] = meshgrid(r,th);

[x y z] = sph2cart(cos(Th),sin(Th),R);

Xi = (R).*cos(Th);

Yi = R.*sin(Th);

ui = ((R.^2-1)/(2*(L+1))).*cos(Th);

vi = ((1-2*R.^2)/(2*(L+1))).*sin(Th);

% figure;contourf(Xi,Yi,ui,100,'LineStyle','none');axis image

% figure;contourf(Xi,Yi,vi,100,'LineStyle','none');axis image

streamslice(x,y,ui,vi);

Jagadeesh Korukonda 2022-12-15

在 MATLAB Online 中打开

Thank you @VBBV

I've made small modification to your code. now its working fine. since my r-domian is [0 1] only.

clc

clear all

close all

nr = 5;

nth = 5;

L = 1;

r =linspace(0,1,nr);

th =linspace(0,pi,nth);

[R,Th] = meshgrid(r,th);

[x y z] = sph2cart(cos(Th),sin(Th),R);

Xi = (R).*cos(Th);

Yi = R.*sin(Th);

ui = ((R.^2-1)/(2*(L+1))).*cos(Th);

vi = ((1-2*R.^2)/(2*(L+1))).*sin(Th);

UI = [fliplr(ui(:,2:end)) ui];

VI = [fliplr(vi(:,2:end)) vi];

X1 = [fliplr(-x(:,2:end)) x];

Y1 = [fliplr(-y(:,2:end)) y];

streamslice(X1,Y1,UI,VI); axis image

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