Hi everyone, thanks for reading! I reduced the 2D Navier Stokes with energy to a problem that looks like this: u_x + v_y = 0 p_x = \frac{1}{Re} u_{yy} p_y = -Ri \ T \mathbf{u} \cdot \nabla T = \frac{1}{Pr} T_{yy} where Re, Ri, Pr are constants and \mathbf{u} = (u, w) and p, T are velo…

Might not be the most efficient solution, but you could multiply your div(u) vector by [0,1] to get the u_y derivative: u_y=dot(np.array([0,1]), div(u) ) I haven’t tried it myself, but this could work. Hope this helps!

Thank you for this! I can’t test this at the moment, but I might be able to use it for T_{yy} :slight_smile: For u_{yy} I not only need to “extract” just that term (which your method might do), but I also need to make sure it doesn’t appear in the equation for p_y. Do you have an idea how I could do…

Hi, thank you! I did see this but I haven’t seen it used in this case, I’ve only seen it be used in Expressions. Could you please tell me how I could use this in my variational formulation? What happens with the test functions then? :slight_smile:

Derivative term in only one direction

variational formulation

bleyerj July 12, 2021, 2:51pm 4

Hi,
u.dx(0) is \partial u /\partial x and u.dx(1) is \partial u / \partial y.

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Action of the time derivative

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Derivative term in only one direction

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