1D linear advection

[Toomyalla]

Hello,

I am trying to change the code of time-dependent DG linear advection using unwinding https://www.firedrakeproject.org/demos/DG_advection.py.html
to solve the problem in 1D and apply Euler for time-updating.

the initial condition is
q(x,0)= x for x<0 .5 and 1-x otherwise.
the boundary condition is q(0,t)=0
and the velocity, u=1

---

from firedrake import *
import matplotlib.pyplot as plt

mesh= UnitIntervalMesh(100)
V = FunctionSpace(mesh, "DQ",0 )

x = SpatialCoordinate(mesh)
u =Constant(1.0)

q = Function(V).interpolate( min_value(x,1-x))
q_init = Function(V).assign(q)

qs=[]

T = 0.5
dt = T/500
dtc = Constant(dt)
q_in = Constant(0.0)


dq_trial = TrialFunction(V)
phi = TestFunction(V)
a = phi*dq_trial*dx

L = dtc*(q*div(phi*u)*dx
          - conditional(u < 0, phi*u*q_in, 0.0)*ds
          - conditional(u > 0, phi*u*q, 0.0)*ds
          - (phi('+') - phi('-'))*(un('+')*q('+') - un('-')*q('-'))*dS)

dq=Function(V)
solv=solve(a == L, dq)
t = 0.0
step = 0
output_freq = 20
while t < T - 0.5*dt:
    solv.solve()
    q.assign(q+dq)

    if step % output_freq == 0:
        qs.append(q.copy(deepcopy=True))
        print("t=", t)

---

I got the error (DQ is supported, but handled incorrectly)
could you please let me know where the problem is?

Thank you

[dham]

I've fixed the formatting of your code.

Can you post the exact error please (i.e. the whole error output you see)?

One thing that may be going on is that we usually refer to the 1D element as DP (i.e. we think of 1D elements as 1-simplices rather than 1-cubes) you could try to make that change and see if something changes.

[Toomyalla]

Thank you,

UFL:ERROR Can't add expressions with different shapes.
Traceback (most recent call last):
File "DG_linear_advection_ex1_2.py", line 11, in
q = Function(V).interpolate( min_value(x,1-x))
File "/home/firedrake/firedrake/src/ufl/ufl/exproperators.py", line 232, in _rsub
return Sum(o, -self)
File "/home/firedrake/firedrake/src/ufl/ufl/algebra.py", line 41, in new
error("Can't add expressions with different shapes.")
File "/home/firedrake/firedrake/src/ufl/ufl/log.py", line 158, in error
raise self._exception_type(self._format_raw(*message))
ufl.log.UFLException: Can't add expressions with different shapes.

---

I've got the same error with DP

[dham]

Ah, your issue is that x is a 1-vector and you're using it as a scalar. The isomorphism between 1-vectors and scalars is so natural that we don't think about it, but computer algebra systems are less good at spotting it. The easiest way to get out of this is to change line 7 to:

x, = SpatialCoordinate(mesh)

The comma after the x has the effect of unpacking the vector so x now becomes the scalar first component of the coordinates, which is what you intended.

[Toomyalla]

Thank you, I put the comma, and it seems to solve the issue.

Now, I get a different error :)

dq=Function(V)
^
SyntaxError: invalid syntax

[connorjward]

This error tends to suggest that there's in fact a syntax error on the line above where the error is thrown. I'm guessing you're missing a bracket in your complicated expression for L.

[Toomyalla]

Thank you all