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.

Action of the time derivative

Topic		Replies	Views
Differentiation of Form variational formulation	2	751	February 22, 2020
Keeping the derivative in one direction variational formulation	4	979	August 13, 2021
Variation formulation for a second order PDE with first order derivative term variational formulation	1	501	March 9, 2021
Add a vector to a scalar - Forward Eular method	4	343	July 21, 2022
Time derivative of the analytical velocity expression variational formulation	1	269	August 31, 2023

Derivative term in only one direction

Related topics