DiscreteNucleationTimeStep Class Reference

Returns a user defined timestep limit for the simulation step right after the introduction of a new nucleus and between nucleation events to control the probability of two or more nuclei appearing in one timestep. More...

#include <DiscreteNucleationTimeStep.h>

Inheritance diagram for DiscreteNucleationTimeStep:

Public Member Functions
	DiscreteNucleationTimeStep (const InputParameters &parameters)
virtual void	initialize () override
virtual void	execute () override
virtual void	finalize () override
virtual PostprocessorValue	getValue () override

Protected Attributes
const DiscreteNucleationInserterBase &	_inserter
	UserObject that manages nucleus insertion and deletion. More...
const Real	_dt_nucleation
	User specified nucleation time step. More...
const DiscreteNucleationInserterBase::NucleusChanges &	_changes_made
	nucleus count changes performed by the inserter More...
const Real &	_rate
	total nucleation rate integrated over teh entire domain More...
Real	_max_lambda
	Maximum total event expectation value that is low enough so that the probability for more than one * nucleation event to occurr in a single timestep is below a user specified value. More...

Detailed Description

Returns a user defined timestep limit for the simulation step right after the introduction of a new nucleus and between nucleation events to control the probability of two or more nuclei appearing in one timestep.

Definition at line 25 of file DiscreteNucleationTimeStep.h.

Constructor & Destructor Documentation

DiscreteNucleationTimeStep()

DiscreteNucleationTimeStep::DiscreteNucleationTimeStep

(

const InputParameters &

parameters

)

Definition at line 37 of file DiscreteNucleationTimeStep.C.

  : GeneralPostprocessor(parameters),
    _inserter(getUserObject<DiscreteNucleationInserterBase>("inserter")),
    _dt_nucleation(getParam<Real>("dt_max")),
    _changes_made(_inserter.getInsertionsAndDeletions()),
    _rate(_inserter.getRate())
{
  //
  // We do a bisection search because math is hard
  // (i.e. probability function is not analytically invertible)
  //
 
  // this is the target value
  const Real p2n = getParam<Real>("p2nucleus");
 
  // initial guess
  _max_lambda = 0.1;
  Real upper_bound = _max_lambda;
  Real lower_bound = 0.0;
 
  // At this point we do not know a proper upper bound for a search interval
  // so we grow our initial guess until we find it (we only allow for a finite
  // number of iterations)
  for (unsigned int i = 0; i < 100; ++i)
  {
    const Real p_upper = 1.0 - (1.0 + upper_bound) * std::exp(-upper_bound);
 
    // we have found a lambda value that results in a p > p2n, this is the upper end of the interval
    if (p_upper > p2n)
      break;
 
    // upper_bound is actually below our target lambda, set it as the new lower
    // bound and double the upper_bound value
    lower_bound = upper_bound;
    upper_bound *= 2.0;
  }
 
  // now that we have an upper and a lower interval bounds we can do a proper bisection
  for (unsigned int i = 0; i < 100; ++i)
  {
    // pick the middle of the current interval
    _max_lambda = (upper_bound - lower_bound) / 2.0 + lower_bound;
 
    // calculate new probability for 2 or more nuclei to appear
    const Real p = 1.0 - (1.0 + _max_lambda) * std::exp(-_max_lambda);
 
    // quit if we zeroed in on the target
    if (MooseUtils::absoluteFuzzyEqual(p, p2n))
      break;
 
    // otherwise adjust interval bounds
    else if (p > p2n)
      upper_bound = _max_lambda;
    else
      lower_bound = _max_lambda;
  }
}

Member Function Documentation

execute()

virtual void DiscreteNucleationTimeStep::execute ( )

inlineoverridevirtual

Definition at line 31 of file DiscreteNucleationTimeStep.h.

{}

finalize()

virtual void DiscreteNucleationTimeStep::finalize ( )

inlineoverridevirtual

Definition at line 32 of file DiscreteNucleationTimeStep.h.

{}

getValue()

PostprocessorValue DiscreteNucleationTimeStep::getValue ( )

overridevirtual

Definition at line 96 of file DiscreteNucleationTimeStep.C.

{
  // check if a nucleus insertion has occurred...
  if (_changes_made.first > 0)
    // and cut back time step for nucleus formation
    return _dt_nucleation;
 
  // otherwise check the total nucleation rate in the domain...
  if (_rate == 0.0)
    // ...and return no limit on the time step if the rate is zero...
    return std::numeric_limits<Real>::max();
  else
    // ...or return the maximum time step that satisfies the bound on the 2+ nuclei probability
    return _max_lambda / _rate;
}

initialize()

virtual void DiscreteNucleationTimeStep::initialize ( )

inlineoverridevirtual

Definition at line 30 of file DiscreteNucleationTimeStep.h.

{}

Member Data Documentation

_changes_made

const DiscreteNucleationInserterBase::NucleusChanges& DiscreteNucleationTimeStep::_changes_made

protected

nucleus count changes performed by the inserter

Definition at line 43 of file DiscreteNucleationTimeStep.h.

Referenced by getValue().

_dt_nucleation

const Real DiscreteNucleationTimeStep::_dt_nucleation

protected

User specified nucleation time step.

Definition at line 40 of file DiscreteNucleationTimeStep.h.

Referenced by getValue().

_inserter

const DiscreteNucleationInserterBase& DiscreteNucleationTimeStep::_inserter

protected

UserObject that manages nucleus insertion and deletion.

Definition at line 37 of file DiscreteNucleationTimeStep.h.

_max_lambda

Real DiscreteNucleationTimeStep::_max_lambda

protected

Maximum total event expectation value that is low enough so that the probability for more than one * nucleation event to occurr in a single timestep is below a user specified value.

Definition at line 53 of file DiscreteNucleationTimeStep.h.

Referenced by DiscreteNucleationTimeStep(), and getValue().

_rate

const Real& DiscreteNucleationTimeStep::_rate

protected

total nucleation rate integrated over teh entire domain

Definition at line 46 of file DiscreteNucleationTimeStep.h.

Referenced by getValue().

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The documentation for this class was generated from the following files:

• phase_field/include/postprocessors/DiscreteNucleationTimeStep.h
• phase_field/src/postprocessors/DiscreteNucleationTimeStep.C