Integration of cross product

Question

Hi,

I'm starting to use FEniCS and i'm modelling a flow machine using FEniCS and i have to solve:

where, omega is a vector, for example ( 0.0, 0.0, 10.0), u is the velocity, W the test function.

So i'm trying to use (first part):

 from dolfin import *
 from dolfin_adjoint import *
 set_log_level(INFO)

 omega = Constant((0.0, 0.0, vel_angular))
 rho = 1.0

 rect = Rectangle(0.0,0.0,1.0,1.0)
 mesh = Mesh(rect,100)

 U = VectorFunctionSpace(mesh, "CG", 3) # velocity function space    -U
 P = FunctionSpace(mesh, "CG", 1)       # pressure function space    -P
 W = MixedFunctionSpace([U, P])         # mixed Taylor-Hood function space

 def BC_1(x, on_boundary):    
     return on_boundary and \
          near(x[0],0.0) or near(x[1],1.0) or near(x[0],1.0)

 def BC_2(x, on_boundary):    
     return on_boundary and \
          near(x[1],0.0)

 Gamma1 = DirichletBC(W.sub(1),0.0,BC_1)    
 Gamma2 = DirichletBC(W.sub(1),10.0,BC_2)   

 bcs = [Gamma1, Gamma2]

 def forward(rho):
   w = Function(W)
   (u, p) = split(w)
   (v, q) = TestFunctions(W)

   F = (2.0*rho*inner(cross(omega,u),v)*dx)

   solve(F == 0, w, bcs)
   return w

 if __name__ == "__main__":
   w   = forward(rho)
   (u, p) = split(w)

Then i get the error:
ufl.log.UFLException: Cross product requires arguments of rank 1

I think this is because i'm trying to use u on the cross product. I've also tried to use:

F=(2.0*rho*inner(-omega[2]*u[1] + omega[2]*u[0] , v)*dx )

Is it possible to solve this kind of functionals that have cross products of valued vectors using fenics?

I really appreciate any help you can provide

Answer 1

Actually, I would expect an error message that refers to the fact that the cross product is defined in 3D but your u is only a 2D vector.

To get started, I suggest you expand the products by hand and write the form coordinatewise.

If you want to use the built-in functionality you should have a look at how the cross product is implemented.

Comments

http://fenicsproject.org/documentation/ufl/1.0-beta/user/form_language.html#cross -- documentation of the cross product

---

Jan, thank you for your answer.

I've created a function to do the cross product:

def my_cross(v,w):
     return (v[1]*w[2]-v[2]*w[1],v[2]*w[0]-v[0]*w[2],v[0]*w[1]-v[1]*w[0])

(...)

F = (2.0*rho*inner(my_cross(omega,u),v)*dx)

and then the error changed to:
"IndexError: tuple index out of range"

Am I doing something wrong?

Edit*: I want to solve it in a 2D domain. So, i'll try to change the my_cross() function

Answer 2

hi，did you solve this problem about how to use outer product? I'm also meet the same problem.
And I have no idea where is wrong.
I'll appreciate your answer.

Comments

Hi, to solve this problem I've changed the function return to a fenics 2D vector, such as:

def my_cross(v,w):
       return as_vector(( v[1]*w[2]-v[2]*w[1],  v[2]*w[0]-v[0]*w[2] ))