Compute Vorticity from Velocity in Dolfinx

General
1

Hello,

I have a 2D velocity field and a pressure field combined in a mixed element function:

velocity_element = VectorElement("Lagrange", self.mesh.ufl_cell(), 2)
pressure_element = FiniteElement("Lagrange", self.mesh.ufl_cell(), 1)

# mixed function space and mixed function
W = FunctionSpace(self.mesh, MixedElement([velocity_element, pressure_element]))
w = Function(W)

How could I compute the vorticity field (scalar field, hence on pressure_element I suppose) from the velocity field ? I have seen a topic about it but it was in FEniCS, not FEniCSx and the syntax seemed to have changed.

Thanks and regards

2

How do you define vorticity?

You can see my comments about 2D vorticity wrt to chosing an appropriate space:

As for moving the ufl-expression in to a function space, see for instance: Gradients and divergences in fenicsx - #4 by Gianna

3

Mathematically, in my case (2D velocity field), the vorticity is a scalar defined everywhere by:

\forall (x,y)\in\Omega\subset\mathbb R^2,\quad\mathbf u(x,y)=u_x(x,y)\mathbf e_x + u_y(x,y)\mathbf e_y\qquad(\text{velocity})\\ \omega(x,y) = \frac{\partial u_y}{\partial x}(x,y) - \frac{\partial u_x}{\partial y}(x,y)\qquad(\text{vorticity})

So I suppose it is computable with ufl.dx or ufl.curl.

4

Since it is 2D, doing something along the lines of

ux, uy = u_n.split(deepcopy=True)
vortex = ux.dx(1)-uy.dx(0)

and putting vortex inside a dolfinx.fem.Expression and interpolate into a suitable function space (DG, velocity degree -1).

1 Like
6

Ok thanks a lot again. Now I have a little and not important problem, but I would like to solve it.

With a Function that is not defined on a mixed function space, I am able to set its name:

vort = Function(V, name="vorticity")

And when written to an xdmf file, I can see in paraview my function is well named.

But when it comes to my mixed-element function w, naming each sub function seems not to work, for example I have this strange result:

w = Function(W, name="mixed_function") # creating my mixed element function (first element correspond to velocity, and second to pressure)
w.sub(0).name = "velocity"  # renaming the first sub function
print(w.sub(0).name) # returns "f_0", but I would like "velocity"

Is that normal ?

7

I cannot reproduce this, consider the following mwe:

from ufl import VectorElement, MixedElement, FiniteElement
from mpi4py import MPI
import dolfinx
mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10)

velocity_element = VectorElement("Lagrange", mesh.ufl_cell(), 2)
pressure_element = FiniteElement("Lagrange", mesh.ufl_cell(), 1)

# mixed function space and mixed function
W = dolfinx.fem.FunctionSpace(mesh, MixedElement([velocity_element, pressure_element]))
w = dolfinx.fem.Function(W)
w.name = "up"
u = w.sub(0)
u.name = "u"
uy = u.sub(1)
print(f"{w.name=} {u.name=} {uy.name=}")

returning

w.name='up' u.name='u' uy.name='u_1'