Triying to solve the Advection Diffusion I get AssertionError: assert expr._ufl_is_terminal_modifier_

variational formulation
1

I would like to implement a crosswind stabilization using the next formula attached and I get AssertionError and I don’t know the reason.

from dolfin import *
import numpy as np
mesh=UnitSquareMesh(32,32)
V_c = FunctionSpace(mesh, "P", 1)
V_u  = VectorFunctionSpace(mesh, "P", 2)

# boundary condition 
betta=Constant(-0.004)
bc_bt= DirichletBC(V_c, Constant(0.0004),  "near(x[0], 1.0) and on_boundary")
bc= [ bc_bt]

# Create velocity Function
u=interpolate(Expression(("vmag*cos(theta)*x[0]","vmag*sin(theta)*x[1]"),domain=mesh, degree=1, theta=pi/6, vmag=3.5), V_u)
# Test and trial functio
v = TestFunction(V_c)
c = TrialFunction(V_c)
c_k = interpolate(Constant(0.0),V_c) # initial guess

# Mesh-related functions
n = FacetNormal(mesh)
h = CellDiameter(mesh)
h_avg = (h('+') + h('-'))/2


diff=Constant(1.2e-5)
# Source term
f = Constant(0.0)
#STABILIZATION CROSSWIND TERMS

alpha=Constant(0.5)
I= Identity(mesh.geometry().dim())

def q(c): 
   return (sqrt(dot(dot(u,grad(c)),dot(u,grad(c))))/sqrt(dot(grad(c),grad(c))))

# Define variational problem for Picard iteration
# Galerkin variational problem

F= (diff*dot(grad(c),grad(v))+inner(u,grad(c))*v)*dx+(betta*c*v)*ds-f*v*dx
# Add crosswind stabilization terms
CWD=(I-(outer(u,u)/sqrt(dot(dot(u,u),dot(u,u)))))
F += dot(dot(0.5*alpha*h_avg*q(c_k)*grad(c),CWD),grad(v))*dx
# Create bilinear and linear forms
a = lhs(F)
L = rhs(F)

# Picard iterations
c = Function(V_c)   # new unknown function 
eps = 1.0           # error measure ||u-u_k||
tol = 1.0E-5        # tolerance
iter = 0            # iteration counter
maxiter = 25        # max no of iterations allowed
while eps > tol and iter < maxiter:
   iter += 1
   solve(a == L, c, bc)
   diff = c.vector().get_local() - c_k.vector().get_local()
   eps = np.linalg.norm(diff, ord=np.Inf)
   c_k.assign(c)   # update for next iteration

I have the problem when i try to solve the system, I think that it is beacuse there are some mistake in the crosswind stabilization when I introduce the terms but I dont know where

AssertionError                            Traceback (most recent call last)
<ipython-input-8-fb3f7f1fa4e7> in <module>
     8 while eps > tol and iter < maxiter:
     9     iter += 1
---> 10     solve(a == L, c, bc)
    11     diff = c.vector().get_local() - c_k.vector().get_local()
    12     eps = np.linalg.norm(diff, ord=np.Inf)

...

~/anaconda3/envs/fenics/lib/python3.8/site-packages/ffc/uflacs/analysis/balancing.py in balance_modified_terminal(expr)
    52     layers = [expr]
    53     while not expr._ufl_is_terminal_:
---> 54         assert expr._ufl_is_terminal_modifier_
    55         expr = expr.ufl_operands[0]
    56         layers.append(expr)

AssertionError:

cw

2

Please format your code by encapsulating it with ```.
Also please make the code a stand-alone example that can be run by anyone. See: Read before posting: How do I get my question answered? for a guidelines for writing a minimal example.

3

Thanks for the correction, it was my first post so I did not know how it works

4

Your code is not a stand-alone example, as several definitions of meshes and other variables are missing, as well as several syntax errors.
Please make the example self contained, using a built in mesh, and try to remove as many lines as possible from your code to locate what is causing the error.

You have also not included the assertion error or which line the assertion error happens in.

5

I think that I have included everything now

6

This should be h as you are only integrating over cells, and there is no notion of restrictions in a cell interior integral

7

Thank you so much! It solve it