def transient_pipe_flow_1D(
npipes, nx, dof, nphases,
pipe_length,
initial_time,
final_time,
initial_time_step,
dt_min,
dt_max,
initial_solution,
impl_python=False
):
# Time Stepper (TS) for ODE and DAE
# DAE - https://en.wikipedia.org/wiki/Differential_algebraic_equation
# https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/
ts = PETSc.TS().create()
#ts.createPython(MyTS(), comm=PETSc.COMM_SELF)
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/index.html
pipes = []
for i in range(npipes):
boundary_type = PETSc.DMDA.BoundaryType.GHOSTED
da = PETSc.DMDA().create([nx], dof=dof, stencil_width=1, stencil_type='star', boundary_type=boundary_type)
da.setFromOptions()
pipes.append(da)
# Create a redundant DM, there is no petsc4py interface (yet)
# so we created our own wrapper
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DMREDUNDANT.html
# dmredundant = PETSc.DM().create()
# dmredundant.setType(dmredundant.Type.REDUNDANT)
# CompositeSimple1D.redundantSetSize(dmredundant, 0, dof)
# dmredundant.setDimension(1)
# dmredundant.setUp()
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DMCOMPOSITE.html
dm = PETSc.DMComposite().create()
for pipe in pipes:
dm.addDM(pipe)
# dm.addDM(dmredundant)
# CompositeSimple1D.compositeSetCoupling(dm)
CompositeSimple1D.registerNewSNES()
ts.setDM(dm)
F = dm.createGlobalVec()
if impl_python:
α0 = initial_solution.reshape((nx,dof))[:, nphases:-1]
pde = Flow(dm, nx, dof, pipe_length, nphases, α0)
ts.setIFunction(pde.evalFunction, F)
else:
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetIFunction.html
assert False, 'C function not implemented yet!'
# ts.setIFunction(CompositeSimple1D.formFunction, F,
# args=(conductivity, source_term, wall_length, temperature_presc))
snes = ts.getSNES()
snes.setUpdate(pde.updateFunction)
x = dm.createGlobalVec()
x[...] = initial_solution
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetDuration.html
ts.setDuration(max_time=final_time, max_steps=None)
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetInitialTimeStep.html
ts.setInitialTimeStep(initial_time=initial_time, initial_time_step=initial_time_step)
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetProblemType.html
ts.setProblemType(ts.ProblemType.NONLINEAR)
ts.setEquationType(ts.EquationType.IMPLICIT)
prev_sol = initial_solution.copy()
# restart = PreStep(prev_sol)
# ts.setPreStep(restart.prestep)
# ts.setPostStep(restart.poststep)
options = PETSc.Options()
options.setValue('-ts_adapt_dt_min', dt_min)
options.setValue('-ts_adapt_dt_max', dt_max)
ts.setFromOptions()
snes = ts.getSNES()
if options.getString('snes_type') in [snes.Type.VINEWTONRSLS, snes.Type.VINEWTONSSLS]:
# if True:
# snesvi = snes.getCompositeSNES(1)
snesvi = snes
xl = np.zeros((nx, dof))
xl[:,:nphases] = -100
xl[:,-1] = 0
xl[:, nphases:-1] = 0
xu = np.zeros((nx, dof))
xu[:,:nphases] = 100
xu[:,-1] = 1000
xu[:, nphases:-1] = 1
xlVec = dm.createGlobalVec()
xuVec = dm.createGlobalVec()
xlVec.setArray(xl.flatten())
xuVec.setArray(xu.flatten())
snesvi.setVariableBounds(xlVec, xuVec)
ts.solve(x)
# while ts.diverged:
# x[...] = prev_sol.copy()
# ts.setInitialTimeStep(initial_time=initial_time, initial_time_step=0.5*initial_time_step)
# ts.solve(x)
final_dt = ts.getTimeStep()
return x, final_dt
def transient_heat_transfer_1D(
npipes, nx,
initial_temperature,
temperature_presc,
conductivity,
source_term,
wall_length,
final_time,
initial_time_step,
impl_python=False
):
# Time Stepper (TS) for ODE and DAE
# DAE - https://en.wikipedia.org/wiki/Differential_algebraic_equation
# https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/
ts = PETSc.TS().create()
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/index.html
#
pipes = []
for i in range(npipes):
pipes.append(PETSc.DMDA().create([nx],dof=1, stencil_width=1, stencil_type='star'))
# Create a redundant DM, there is no petsc4py interface (yet)
# so we created our own wrapper
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DMREDUNDANT.html
dmredundant = PETSc.DM().create()
dmredundant.setType(dmredundant.Type.REDUNDANT)
HeatTransfer1D.redundantSetSize(dmredundant, 0, 1)
dmredundant.setDimension(1)
dmredundant.setUp()
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DMCOMPOSITE.html
dm = PETSc.DMComposite().create()
for pipe in pipes:
dm.addDM(pipe)
dm.addDM(dmredundant)
HeatTransfer1D.compositeSetCoupling(dm)
ts.setDM(dm)
F = dm.createGlobalVec()
if impl_python:
ode = Heat(dm, temperature_presc, conductivity, source_term, wall_length)
ts.setIFunction(ode.evalFunction, F)
else:
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetIFunction.html
ts.setIFunction(HeatTransfer1D.formFunction, F,
args=(conductivity, source_term, wall_length, temperature_presc))
x = dm.createGlobalVec()
x[...] = initial_temperature
#HeatTransfer1D.formInitGuess(x, dm, initial_temperature)
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetDuration.html
ts.setDuration(max_time=final_time, max_steps=None)
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetExactFinalTime.html
ts.setExactFinalTime(ts.ExactFinalTimeOption.STEPOVER)
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetInitialTimeStep.html
ts.setInitialTimeStep(initial_time=0.0, initial_time_step=initial_time_step)
# http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSSetProblemType.html
ts.setProblemType(ts.ProblemType.NONLINEAR)
# Another way to set the solve type is through PETSc.Options()
#ts.setType(ts.Type.CRANK_NICOLSON)
#ts.setType(ts.Type.THETA)
#ts.setTheta(theta=0.9999)
#ts.setType(ts.Type.EIMEX) # http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TSEIMEX.html
#ts.setType(ts.Type.BDF )
ts.setFromOptions()
ts.solve(x)
return x
