Adaptive burnup stepsize selection using control theory for 2-D lattice depletion simulations

• Automated and adaptive depletion stepsize methodology using control theory.
• Standard predictor–corrector method is leveraged to provide convergence residual.
• Monitoring the L2 relative error norm of the neutron flux provides stepsize control.
• Stepsize controllers are parameterized to provide optimal behavior.
• Integrating controller performs well for fuel lattices with and without burnable absorbers.

A control theory approach is adopted to determine the temporal discretization during two-dimensional lattice physics depletion simulations. Two primary applications of automated and adaptive stepsize control are identified: (i) the presence of strong absorbers such as gadolinium, where the accurate burnout of the isotopes requires a depletion stepsize smaller than typically required, and (ii) high fidelity multiphysics simulations, e.g. loosely coupled physics, where the coupled physics are nonlinear in time and stepsize changes may be necessary to obtain an accurate coupled solution. A conventional predictor–corrector method is used to address the nonlinearity of the nuclide transmutation and neutron flux. An adaptive stepsize method is developed based on monitoring the one-group scalar neutron flux at both the predictor and corrector steps to approximate the convergence residual of the nonlinear solution. A user-specified tolerance on the L2 relative error norm of the scalar neutron flux is utilized by the stepsize controller. Controllers that include integral, proportional, and/or derivative components are investigated and parameterized using Latin hypercube sampling of the controller input parameters. Three distinct fuel loadings of pressurized water reactor 17 × 17 fuel pin assemblies are considered, including no burnable absorbers, Integral Fuel Burnable Absorber, and gadolinium fuel pins. The required depletion stepsizes, as predicted throughout the cycle by the controller, are compared with a very small stepsize (0.01 MW d/kgHM) reference solution and a solution obtained by a typical rule of thumb depletion stepsize sequence.