f = -MU * Laplacian + Advection + gradPres
bc = DirichletBC(W.sub(0), u0, boundary)
bcs = [bc]
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
mu = Constant(1e0)
n = FacetNormal(mesh)
h = CellSize(mesh)
h_avg = avg(h)
d = 0
u_k, p_k = common.Stokes(V, Q, u0, Expression(("0", "0")), [1, 1, mu])
p_k.vector()[:] = p_k.vector().array() - np.max(p_k.vector().array())
uOld = np.concatenate((u_k.vector().array(), p_k.vector().array()), axis=0)
r = IO.arrayToVec(uOld[:-1])
a11 = mu * inner(grad(v), grad(u)) * dx + inner(
(grad(u) * u_k), v) * dx + (1 / 2) * div(u_k) * inner(
u, v) * dx - (1 / 2) * inner(u_k, n) * inner(u, v) * ds
a12 = div(v) * p * dx
a21 = div(u) * q * dx
L1 = inner(v, f) * dx
a = a11 - a12 - a21
r11 = mu * inner(grad(v), grad(u_k)) * dx + inner(
(grad(u_k) * u_k), v) * dx + (1 / 2) * div(u_k) * inner(
u_k, v) * dx - (1 / 2) * inner(u_k, n) * inner(u_k, v) * ds
r12 = div(v) * p_k * dx
# MU = Constant(0.01)
# MU = 1000.0
MU = 1.0
bcc = DirichletBC(W.sub(0), u0, boundary)
bcs = [bcc]
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
f = -MU * Laplacian + Advection + gradPres
n = FacetNormal(mesh)
h = CellSize(mesh)
h_avg = avg(h)
d = 0
u_k, p_k = common.Stokes(V, Q, u0, f, [1, 1, MU], FS="DG", InitialTol=1e-6)
# p_k.vector()[:] = p_k.vector().array()
pConst = -assemble(p_k * dx) / assemble(ones * dx)
p_k.vector()[:] += pConst
# u_k = Function(V)
# p_k = Function(Q)
# plot(u_k)
# plot(p_k)
uOld = np.concatenate((u_k.vector().array(), p_k.vector().array()), axis=0)
r = IO.arrayToVec(uOld)
a11 = MU * inner(grad(v), grad(u)) * dx(mesh) + inner(
(grad(u) * u_k), v) * dx(mesh) + (1. / 2) * div(u_k) * inner(
u, v) * dx(mesh) - (1. / 2) * inner(u_k, n) * inner(u,
v) * ds(mesh)
a12 = div(v) * p * dx
MU = 10.0
bcc = DirichletBC(W.sub(0),u0, boundary)
bcs = [bcc]
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
f = -MU*Laplacian+gradPres
n = FacetNormal(mesh)
h = CellSize(mesh)
h_avg =avg(h)
d = 0
u_k,p_k = common.Stokes(V,Q,u0,f,[1,1,MU])
uOld = np.concatenate((u_k.vector().array(),p_k.vector().array()), axis=0)
r = IO.arrayToVec(uOld)
a11 = MU*inner(grad(v), grad(u))*dx + inner((grad(u)*u_k),v)*dx + (1/2)*div(u_k)*inner(u,v)*dx- (1/2)*inner(u_k,n)*inner(u,v)*ds
a12 = div(v)*p*dx
a21 = div(u)*q*dx
L1 = inner(v, f)*dx
a = a11-a12-a21
r11 = MU*inner(grad(v), grad(u_k))*dx + inner((grad(u_k)*u_k),v)*dx + (1/2)*div(u_k)*inner(u_k,v)*dx- (1/2)*inner(u_k,n)*inner(u_k,v)*ds
r12 = div(v)*p_k*dx
r21 = div(u_k)*q*dx
RHSform = r11-r12-r21
Advection = Expression((
"x[0]*pow(exp(x[2]),2)+x[0]*cos(x[0])*pow(sin(x[1]),2)*exp(x[2])",
"-cos(x[1])*sin(x[1])*pow(exp(x[2]),2)+cos(x[0])*cos(x[1])*sin(x[1])*exp(x[2])",
"-x[0]*pow(sin(x[1]),2)*exp(x[2])*sin(x[0])+pow(cos(x[1]),2)*exp(x[2])*cos(x[0])"
))
gradPres = Expression(
("cos(x[1])*cos(x[0])*exp(x[2])", "-sin(x[1])*sin(x[0])*exp(x[2])",
"sin(x[0])*cos(x[1])*exp(x[2])"))
f = Laplacian + Advection + gradPres
n = FacetNormal(mesh)
h = CellSize(mesh)
h_avg = avg(h)
d = 0
u_k, p_k = common.Stokes(V, Q, u0, Laplacian + gradPres, [1, 1, MU])
uOld = np.concatenate((u_k.vector().array(), p_k.vector().array()), axis=0)
r = IO.arrayToVec(uOld)
a11 = MU * inner(grad(v), grad(u)) * dx + inner(
(grad(u) * u_k), v) * dx + (1 / 2) * div(u_k) * inner(
u, v) * dx - (1 / 2) * inner(u_k, n) * inner(u, v) * ds
a12 = div(v) * p * dx
a21 = div(u) * q * dx
L1 = inner(v, f) * dx
a = a11 - a12 - a21
r11 = MU * inner(grad(v), grad(u_k)) * dx + inner(
(grad(u_k) * u_k), v) * dx + (1 / 2) * div(u_k) * inner(
u_k, v) * dx - (1 / 2) * inner(u_k, n) * inner(u_k, v) * ds
