def FluidNonLinearSetup(Pressure,mu, u_k):
MO.PrintStr("Preconditioning Fluid linear setup",3,"=")
# parameters['linear_algebra_backend'] = 'uBLAS'
p = TrialFunction(Pressure)
q = TestFunction(Pressure)
mesh = Pressure.mesh()
N = FacetNormal(Pressure.mesh())
h = CellSize(Pressure.mesh())
h_avg =avg(h)
alpha = 10.0
gamma =10.0
tic()
if Pressure.__str__().find("CG") == -1:
Fp = assemble(mu*(jump(q)*jump(p)*dx(mesh)) \
+ inner(inner(grad(p),u_k),q)*dx(mesh)- (1./2)*inner(u_k,N)*inner(q,p)*ds(mesh) \
-(1./2)*(inner(u_k('+'),N('+'))+inner(u_k('-'),N('-')))*avg(inner(q,p))*ds(mesh) \
-dot(avg(q),dot(outer(p('+'),N('+'))+outer(p('-'),N('-')),avg(u_k)))*dS(Pressure.mesh()))
else:
if mesh.topology().dim() == 2:
Fp = assemble(mu*inner(grad(q), grad(p))*dx(mesh)+inner((u_k[0]*grad(p)[0]+u_k[1]*grad(p)[1]),q)*dx(mesh) + (1./2)*div(u_k)*inner(p,q)*dx(mesh) + (1./2)*(u_k[0]*N[0]+u_k[1]*N[1])*inner(p,q)*ds(mesh))
else:
Fp = assemble(mu*inner(grad(q), grad(p))*dx(mesh)+inner((u_k[0]*grad(p)[0]+u_k[1]*grad(p)[1]+u_k[2]*grad(p)[2]),q)*dx(mesh) + (1./2)*div(u_k)*inner(p,q)*dx(mesh) - (1./2)*(u_k[0]*N[0]+u_k[1]*N[1]+u_k[2]*N[2])*inner(p,q)*ds(mesh))# + (-mu*inner(grad(q),N)*p + inner(u_k, N)*q*p)*ds(2))
Fp = CP.Assemble(Fp)
print ("{:40}").format("DG convection-diffusion assemble, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
tic()
kspFp= NSprecondSetup.PCDKSPnonlinear(Fp)
print ("{:40}").format("Non-linear fluid precond, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
print "\n\n"
return kspFp, Fp
def FluidNonLinearSetup(Pressure, mu, u_k):
MO.PrintStr("Preconditioning Fluid linear setup", 3, "=")
parameters['linear_algebra_backend'] = 'uBLAS'
p = TrialFunction(Pressure)
q = TestFunction(Pressure)
mesh = Pressure.mesh()
N = FacetNormal(Pressure.mesh())
h = CellSize(Pressure.mesh())
h_avg = avg(h)
alpha = 10.0
gamma = 10.0
tic()
Fp = assemble(mu*(inner(grad(q), grad(p))*dx(mesh) \
- inner(avg(grad(q)), outer(p('+'),N('+'))+outer(p('-'),N('-')))*dS (Pressure.mesh())\
- inner(outer(q('+'),N('+'))+outer(q('-'),N('-')), avg(grad(p)))*dS (Pressure.mesh())\
+
alpha/h_avg*inner(outer(q('+'),N('+'))+outer(q('-'),N('-')),outer(p('+'),N('+'))+outer(p('-'),N('-')))*dS(Pressure.mesh()) \
- inner(outer(q,N), grad(p))*ds(mesh) \
- inner(grad(q), outer(p,N))*ds(mesh) \
+ gamma/h*inner(q,p)*ds(mesh)) \
+ inner(inner(grad(p),u_k),q)*dx(mesh)- (1/2)*inner(u_k,N)*inner(q,p)*ds(mesh) \
-(1/2)*(inner(u_k('+'),N('+'))+inner(u_k('-'),N('-')))*avg(inner(q,p))*ds(mesh) \
-dot(avg(q),dot(outer(p('+'),N('+'))+outer(p('-'),N('-')),avg(u_k)))*dS(Pressure.mesh()))
Fp = PETSc.Mat().createAIJ(size=Fp.sparray().shape,
csr=(Fp.sparray().indptr, Fp.sparray().indices,
Fp.sparray().data))
print("{:40}"
).format("DG convection-diffusion assemble, time: "), " ==> ", (
"{:4f}").format(
toc()), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
tic()
kspFp = NSprecondSetup.PCDKSPnonlinear(Fp)
print("{:40}").format("Non-linear fluid precond, time: "), " ==> ", (
"{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
print "\n\n"
return kspFp, Fp
