Burgers equation tutorial

[miguelmoyers]

Hello All,

I am a complete novice to Firedrake. I just installed it yesterday. I want to use it for one of my courses. I've been working through the tutorials and I ran into some issues. In the Burgers equation one, I changed the initial condition to ic = project(as_vector((sin(2pix[0])+0.5sin(pix[0]), 0)), V). For some reason, I get the absolute value of the function. Am I missing something? What is as_vector() doing? I've been at it for a couple of hours and cannot find anything online. Sorry if it is a very simple question.
Thank you for your help.

Miguel

[colinjcotter]

Hi Miguel, as_vector turns a list of expressions into a UFL symbolic representation of a vector field with the list contents given the Cartesian components. all the best cjc On 14 Oct 2022, at 07:42, miguelmoyers ***@***.***> wrote:  Hello All, I am a complete novice to Firedrake. I just installed it yesterday. I want to use it for one of my courses. I've been working through the tutorials and I ran into some issues. In the Burgers equation one, I changed the initial condition to ic = project(as_vector((sin(2pix[0])+0.5sin(pix[0]), 0)), V). For some reason, I get the absolute value of the function. Am I missing something? What is as_vector() doing? I've been at it for a couple of hours and cannot find anything online. Sorry if it is a very simple question. Thank you for your help. Miguel — Reply to this email directly, view it on GitHub<#2585>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABOSV4TEJTQR7YIT3QDJVMDWDD6FXANCNFSM6AAAAAARE54YWU>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[miguelmoyers]

Hello Colin,

That is what I thought. Still, when I project the initial condition into V, it seems it is taking the absolute value of the function, any idea why?
I attach a plot of the initial condition and the code I am using (which is the one from the tutorial but with a different initial condition).

from firedrake import *
import matplotlib.pyplot as plt
n = 30
mesh = UnitSquareMesh(n, n)

V = VectorFunctionSpace(mesh, "CG", 2)
V_out = VectorFunctionSpace(mesh, "CG", 1)

u_ = Function(V, name="Velocity")
u = Function(V, name="VelocityNext")

v = TestFunction(V)

x= SpatialCoordinate(mesh)
ic = project(as_vector([sin(2pix[0])+0.5sin(pix[0]), 0]), V)

u_.assign(ic)
u.assign(ic)

nu = 0.00001

timestep = 1.0/n

F = (inner((u - u_)/timestep, v)
+ inner(dot(u,nabla_grad(u)), v) + nu*inner(grad(u), grad(v)))*dx

t = 0.0
end = 0.5
while (t <= end):
solve(F == 0, u)
u_.assign(u)
t += timestep
uforplot=project(u,V_out)
trisurf(uforplot)
plt.show()
plt.close()