#
p+=dp
U=U_new
print("U:",inf(U),sup(U))
print("P:",inf(p),sup(p))
p_pos=clip(p,small)
gg=grad(U)
vol=gg[0,0]+gg[1,1]+U[0]/r
gamma=sqrt(2*((gg[0,0]-vol/3)**2+(gg[1,1]-vol/3)**2+(U[0]/r-vol/3)**2+(gg[1,0]+gg[0,1])**2/2))
m=whereNegative(eta*gamma-alpha*p_pos)
eta_d=m*eta+(1.-m)*alpha*p_pos/(gamma+small)
print("viscosity =",inf(eta_d),sup(eta_d))
dev_stress=eta_d*(symmetric(gg)-2./3.*vol*kronecker(dom))
#
# step size control:
#
len=inf(dom.getSize())
dt1=inf(dom.getSize()/(length(U)+small))
dt2=inf(0.5*ro*(len**2)/eta_d)
dt=dt1*dt2/(dt1+dt2)
print("new step size = ",dt)
#
# update geometry
#
dom.setX(dom.getX()+U*dt)
t=t+dt
if (istep-1)%w_step==0:saveVTK("u.%d.vtu"%((istep-1)/w_step),p=p,eta=eta_d,U=U_star,U_star=U_star,gamma=gamma)
if istep == 3: 1/0
x = Function(dom).getX()
if DIM == 2:
V = OMEGA0 * (x[0] * [0, -1] + x[1] * [1, 0])
else:
V = OMEGA0 * (x[0] * [0, cos(ALPHA), 0] + x[1] *
[-cos(ALPHA), 0, sin(ALPHA)] + x[2] * [0., -sin(ALPHA), 0.])
#===================
fc = TransportPDE(dom, num_equations=1, theta=THETA)
x = Function(dom).getX()
fc.setValue(M=Scalar(1., Function(dom)), C=V)
#==============
if TEST_SUPG:
supg = LinearSinglePDE(dom)
supg.setValue(D=1.)
supg.setSolverMethod(supg.LUMPING)
dt_supg = inf(dom.getSize() / length(V))
u_supg = u0 * 1.
c = 0
# saveVTK("u.%s.vtu"%c,u=u0)
fc.setInitialSolution(u0)
t = T0
print("QUALITY FCT: time = %s pi" % (t / pi), inf(u0), sup(u0), integrate(u0))
while t < T_END:
print("time step t=", t + dt)
u = fc.solve(dt, verbose=True)
print("QUALITY FCT: time = %s pi" % (t + dt / pi), inf(u), sup(u),
integrate(u))
if TEST_SUPG:
#========== supg tests ================
nn = max(ceil(dt / dt_supg), 1.)
#
p+=dp
U=U_new
print("U:",inf(U),sup(U))
print("P:",inf(p),sup(p))
p_pos=clip(p,small)
gg=grad(U)
vol=gg[0,0]+gg[1,1]+U[0]/r
gamma=sqrt(2*((gg[0,0]-vol/3)**2+(gg[1,1]-vol/3)**2+(U[0]/r-vol/3)**2+(gg[1,0]+gg[0,1])**2/2))
m=whereNegative(eta*gamma-alpha*p_pos)
eta_d=m*eta+(1.-m)*alpha*p_pos/(gamma+small)
print("viscosity =",inf(eta_d),sup(eta_d))
dev_stress=eta_d*(symmetric(gg)-2./3.*vol*kronecker(dom))
#
# step size control:
#
len=inf(dom.getSize())
dt1=inf(dom.getSize()/(length(U)+small))
dt2=inf(0.5*ro*(len**2)/eta_d)
dt=dt1*dt2/(dt1+dt2)
print("new step size = ",dt)
#
# update geometry
#
dom.setX(dom.getX()+U*dt)
t=t+dt
if (istep-1)%w_step==0:saveVTK("u.%d.vtu"%((istep-1)/w_step),p=p,eta=eta_d,U=U_star,U_star=U_star,gamma=gamma)
if istep == 3: 1/0
V = OMEGA0 * (x[0] * [0, -1] + x[1] * [1, 0])
else:
V = OMEGA0 * (x[0] * [0, cos(ALPHA), 0] + x[1] *
[-cos(ALPHA), 0, sin(ALPHA)] + x[2] * [0., -sin(ALPHA), 0.])
#===================
fc = TransportPDE(dom, num_equations=1, theta=THETA)
x = Function(dom).getX()
fc.setValue(M=Scalar(1., Function(dom)),
C=V,
A=-Scalar(E, Function(dom)) * kronecker(dom))
#==============
if TEST_SUPG:
supg = LinearSinglePDE(dom)
supg.setValue(D=1.)
supg.setSolverMethod(supg.LUMPING)
dt_supg = 1. / (1. / inf(dom.getSize() / length(V)) +
1. / inf(dom.getSize()**2 / E)) * 0.3
u_supg = u0 * 1.
c = 0
saveVTK("u.%s.vtu" % c, u=u0)
fc.setInitialSolution(u0)
t = T0
while t < T_END:
print("time step t=", t + dt)
u = fc.solve(dt)
if TEST_SUPG:
#========== supg tests ================
nn = max(ceil(dt / dt_supg), 1.)
dt2 = dt / nn
nnn = 0
x=Function(dom).getX()
if DIM == 2:
V=OMEGA0*(x[0]*[0,-1]+x[1]*[1,0])
else:
V=OMEGA0*(x[0]*[0,cos(ALPHA),0]+x[1]*[-cos(ALPHA),0,sin(ALPHA)]+x[2]*[0.,-sin(ALPHA),0.])
#===================
fc=TransportPDE(dom,num_equations=1,theta=THETA)
x=Function(dom).getX()
fc.setValue(M=Scalar(1.,Function(dom)),C=V,A=-Scalar(E,Function(dom))*kronecker(dom))
#==============
if TEST_SUPG:
supg=LinearSinglePDE(dom)
supg.setValue(D=1.)
supg.setSolverMethod(supg.LUMPING)
dt_supg=1./(1./inf(dom.getSize()/length(V))+1./inf(dom.getSize()**2/E))*0.3
u_supg=u0*1.
c=0
saveVTK("u.%s.vtu"%c,u=u0)
fc.setInitialSolution(u0)
t=T0
while t<T_END:
print("time step t=",t+dt)
u=fc.solve(dt)
if TEST_SUPG:
#========== supg tests ================
nn=max(ceil(dt/dt_supg),1.)
dt2=dt/nn
nnn=0
while nnn<nn :
TOL = 1.0e-5
max_iter = 400
verbose = True
useUzawa = True
#define mesh
l0 = 0.9142
l1 = 1.0
n0 = 200
n1 = 200
mesh = Rectangle(l0=l0, l1=l1, order=2, n0=n0, n1=n1)
#get mesh dimensions
numDim = mesh.getDim()
#get element size
h = Lsup(mesh.getSize())
#level set parameters
tolerance = 1.0e-6
reinit_max = 30
reinit_each = 3
alpha = 1
smooth = alpha * h
#boundary conditions
x = mesh.getX()
#left + bottom + right + top
b_c = whereZero(x[0]) * [1.0, 0.0] + whereZero(x[1]) * [1.0, 1.0] + whereZero(
x[0] - l0) * [1.0, 0.0] + whereZero(x[1] - l1) * [1.0, 1.0]
velocity = Vector(0.0, ContinuousFunction(mesh))
TOL = 1.0e-5 max_iter=400 verbose=True useUzawa=True #define mesh l0=0.9142 l1=1.0 n0=200 n1=200 mesh=Rectangle(l0=l0, l1=l1, order=2, n0=n0, n1=n1) #get mesh dimensions numDim = mesh.getDim() #get element size h = Lsup(mesh.getSize()) #level set parameters tolerance = 1.0e-6 reinit_max = 30 reinit_each = 3 alpha = 1 smooth = alpha*h #boundary conditions x = mesh.getX() #left + bottom + right + top b_c = whereZero(x[0])*[1.0,0.0] + whereZero(x[1])*[1.0,1.0] + whereZero(x[0]-l0)*[1.0,0.0] + whereZero(x[1]-l1)*[1.0,1.0] velocity = Vector(0.0, ContinuousFunction(mesh)) pressure = Scalar(0.0, ContinuousFunction(mesh))
x=Function(dom).getX()
if DIM == 2:
V=OMEGA0*(x[0]*[0,-1]+x[1]*[1,0])
else:
V=OMEGA0*(x[0]*[0,cos(ALPHA),0]+x[1]*[-cos(ALPHA),0,sin(ALPHA)]+x[2]*[0.,-sin(ALPHA),0.])
#===================
fc=TransportPDE(dom,num_equations=1,theta=THETA)
x=Function(dom).getX()
fc.setValue(M=Scalar(1.,Function(dom)),C=V)
#==============
if TEST_SUPG:
supg=LinearSinglePDE(dom)
supg.setValue(D=1.)
supg.setSolverMethod(supg.LUMPING)
dt_supg=inf(dom.getSize()/length(V))
u_supg=u0*1.
c=0
# saveVTK("u.%s.vtu"%c,u=u0)
fc.setInitialSolution(u0)
t=T0
print("QUALITY FCT: time = %s pi"%(t/pi),inf(u0),sup(u0),integrate(u0))
while t<T_END:
print("time step t=",t+dt)
u=fc.solve(dt, verbose=True)
print("QUALITY FCT: time = %s pi"%(t+dt/pi),inf(u),sup(u),integrate(u))
if TEST_SUPG:
#========== supg tests ================
nn=max(ceil(dt/dt_supg),1.)
dt2=dt/nn
