Hi everyone!

I’m trying to plot the gradient of a functional of kinetic energy of a Navier-Stokes’s solution but I get some errors.

My code is

```
from fenics import *
from mshr import *
from dolfin import *
from dolfin_adjoint import *
T = 90
num_steps = int(T)*25
dtn = T / num_steps
y_h= 11
rho = 1 # density
U0=1 #initial horizontal velocity
Re=70 #Reynold's number
D=1
mu=rho*U0*D/Re
channel = Rectangle(Point(-10.0, -y_h), Point(20.0, y_h))
cylinder = Circle(Point(0.0, 0.1), 0.5,35)
domain = channel - cylinder
mesh = generate_mesh(domain, 35)
bcu_inflow = DirichletBC(V, Expression(inflow_profile, degree=2), inflow)
bcu_walls = DirichletBC(V, Constant((0, 0)), walls)
bcu_cylinder = DirichletBC(V, Constant((0, 0)), cylinder)
bcp_outflow = DirichletBC(Q, Constant(0), outflow)
bcu = [bcu_inflow, bcu_walls, bcu_cylinder]
bcp = [bcp_outflow]
u= TrialFunction(V)
v= TestFunction(V)
#v, q= TestFunctions(W)
p=TrialFunction(Q)
q= TestFunction(Q)
u_n = Function(V)
u_ = Function(V)
p_n = Function(Q)
p_ = Function(Q)
# Define expressions used in variational forms
U = 0.5*(u_n + u)
n = FacetNormal(mesh)
f = Constant((0, 0))
k = Constant(dtn)
mu = Constant(mu)
def epsilon(u):
return sym(nabla_grad(u))
# Define stress tensor
def sigma(u, p):
return 2*mu*epsilon(u) - p*Identity(len(u))
F1 = rho*dot((u - u_n) / k, v)*dx \
+ rho*dot(dot(u_n, nabla_grad(u_n)), v)*dx \
+ inner(sigma(U, p_n), epsilon(v))*dx \
+ dot(p_n*n, v)*ds - dot(mu*nabla_grad(U)*n, v)*ds \
- dot(f, v)*dx
a1 = lhs(F1)
L1 = rhs(F1)
# Define variational problem for step 2
a2 = dot(nabla_grad(p), nabla_grad(q))*dx
L2 = dot(nabla_grad(p_n), nabla_grad(q))*dx - (1/k)*div(u_)*q*dx
# Define variational problem for step 3
a3 = dot(u, v)*dx
L3 = dot(u_, v)*dx - k*dot(nabla_grad(p_ - p_n), v)*dx
# Assemble matrices
A1 = assemble(a1)
A2 = assemble(a2)
A3 = assemble(a3)
# Apply boundary conditions to matrices
[bc.apply(A1) for bc in bcu]
[bc.apply(A2) for bc in bcp]
for n_steps in range(500):
t += dtn
# Step 1: Tentative velocity step
b1 = assemble(L1)
[bc.apply(b1) for bc in bcu]
solve(A1, u_.vector(), b1, 'bicgstab', 'hypre_amg')
# Step 2: Pressure correction step
b2 = assemble(L2)
[bc.apply(b2) for bc in bcp]
solve(A2, p_.vector(), b2, 'bicgstab', 'hypre_amg')
# Step 3: Velocity correction step
b3 = assemble(L3)
solve(A3, u_.vector(), b3, 'cg', 'sor')
# Update previous solution
u_n.assign(u_)
p_n.assign(p_)
J = assemble(inner(u_, u_)*dx)
dJdnu = compute_gradient(J,Control(mu), options={"riesz_representation": "L2"})
gra = File('gradient.pvd')
gra << dJdnu
```

The error is

```
RuntimeError: Unable to cast Python instance to C++ type (compile in debug mode for details)
```

If I try plot(dJdnu), I’ll get

```
RuntimeError: Expecting a mesh as keyword argument
```

I tried this without “L2 representation” with same result.

Can anyone suggest any ideas?

Thank you!