# openmc.deplete.CELIIntegrator¶

class openmc.deplete.CELIIntegrator(operator, timesteps, power=None, power_density=None, source_rates=None, timestep_units='s', solver='cram48')[source]

Deplete using the CE/LI CFQ4 algorithm.

Implements the CE/LI Predictor-Corrector algorithm using the fourth order commutator-free integrator.

“CE/LI” stands for constant extrapolation on predictor and linear interpolation on corrector. This algorithm is mathematically defined as:

\begin{aligned} \mathbf{n}_{i+1}^p &= \exp \left ( h \mathbf{A}(\mathbf{n}_i ) \right ) \\ \mathbf{n}_{i+1} &= \exp \left( \frac{h}{12} \mathbf{A}(\mathbf{n}_i) + \frac{5h}{12} \mathbf{A}(\mathbf{n}_{i+1}^p) \right) \exp \left( \frac{5h}{12} \mathbf{A}(\mathbf{n}_i) + \frac{h}{12} \mathbf{A}(\mathbf{n}_{i+1}^p) \right) \mathbf{n}_i. \end{aligned}
Parameters
• operator (openmc.deplete.TransportOperator) – Operator to perform transport simulations

• timesteps (iterable of float or iterable of tuple) – Array of timesteps. Note that values are not cumulative. The units are specified by the timestep_units argument when timesteps is an iterable of float. Alternatively, units can be specified for each step by passing an iterable of (value, unit) tuples.

• power (float or iterable of float, optional) – Power of the reactor in [W]. A single value indicates that the power is constant over all timesteps. An iterable indicates potentially different power levels for each timestep. For a 2D problem, the power can be given in [W/cm] as long as the “volume” assigned to a depletion material is actually an area in [cm^2]. Either power, power_density, or source_rates must be specified.

• power_density (float or iterable of float, optional) – Power density of the reactor in [W/gHM]. It is multiplied by initial heavy metal inventory to get total power if power is not speficied.

• source_rates (float or iterable of float, optional) –

Source rate in [neutron/sec] for each interval in timesteps

New in version 0.12.1.

• timestep_units ({'s', 'min', 'h', 'd', 'MWd/kg'}) – Units for values specified in the timesteps argument. ‘s’ means seconds, ‘min’ means minutes, ‘h’ means hours, and ‘MWd/kg’ indicates that the values are given in burnup (MW-d of energy deposited per kilogram of initial heavy metal).

• solver (str or callable, optional) –

If a string, must be the name of the solver responsible for solving the Bateman equations. Current options are:

• cram16 - 16th order IPF CRAM

• cram48 - 48th order IPF CRAM [default]

If a function or other callable, must adhere to the requirements in solver.

New in version 0.12.

Variables
• operator (openmc.deplete.TransportOperator) – Operator to perform transport simulations

• chain (openmc.deplete.Chain) – Depletion chain

• timesteps (iterable of float) – Size of each depletion interval in [s]

• source_rates (iterable of float) – Source rate in [W] or [neutron/sec] for each interval in timesteps

• solver (callable) –

Function that will solve the Bateman equations $$\frac{\partial}{\partial t}\vec{n} = A_i\vec{n}_i$$ with a step size $$t_i$$. Can be configured using the solver argument. User-supplied functions are expected to have the following signature: solver(A, n0, t) -> n1 where

New in version 0.12.

__call__(bos_conc, rates, dt, source_rate, _i=None)[source]

Perform the integration across one time step

Parameters
• bos_conc (numpy.ndarray) – Initial concentrations for all nuclides in [atom]

• rates (openmc.deplete.ReactionRates) – Reaction rates from operator

• dt (float) – Time in [s] for the entire depletion interval

• source_rate (float) – Power in [W] or source rate in [neutron/sec]

• _i (int, optional) – Current iteration count. Not used

Returns

• proc_time (float) – Time spent in CRAM routines for all materials in [s]

• conc_list (list of numpy.ndarray) – Concentrations at each of the intermediate points with the final concentration as the last element

• op_results (list of openmc.deplete.OperatorResult) – Eigenvalue and reaction rates from intermediate transport simulation

__iter__()

Return pair of time step in [s] and source rate in [W] or [neutron/sec]

__len__()

Return integer number of depletion intervals

integrate(final_step=True)

Perform the entire depletion process across all steps

Parameters

final_step (bool, optional) –

Indicate whether or not a transport solve should be run at the end of the last timestep.

New in version 0.12.1.