How to calculate the gradient of 3D velocity

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Xinchen Zhang 2020-8-21

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https://ww2.mathworks.cn/matlabcentral/answers/582575-how-to-calculate-the-gradient-of-3d-velocity

回答： Bjorn Gustavsson 2020-8-21

Let's say the "wind.mat" in matlab. I was supposed to get 9 tensors of the velocity gradients, du/dx, du/dy, du/dz, dv/dx, dv/dy, dv/dz, dw/dx, dw/dy, dw/dz.

I calculate following dudx=gradient(u)./gradient(x), dudy=gradient(u)./gradient(y) ...

but the gradient(y)=0 and gradient(z)=0 for this equally-spaced mat, results in a infinity value in the du/dy tensor.

Anyone can help me to correct the script for the gradient calculation?

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KSSV 2020-8-21

Read the documentation properly......if you provide an array, you will get all the components at once.

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Answer 1

Bjorn Gustavsson 2020-8-21

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Unfortunately you will have to do something like this:

[dudx,dudy,dudz] = gradient(u,squeeze(x(1,:,1)),squeeze(y(:,1,1)),squeeze(z(1,1,:)));

If you want the gradients of the wind-vector components in wind.mat.

Two additional points to mention about gradient:

1, it does not give a properly centred difference approximation to the gradient for cases where the coordinates are not varying linearly. It just uses a naive centred difference-scheme.

2, the above obviously requires the grid to be plaid.

HTH