An adaptive time step control scheme for the transient diffusion equation

The stability and accuracy of an adaptive time step control scheme are analyzed for the transient diffusion equation. This scheme is based on the commonly-implemented backward difference discretization of the diffusion equation and recommends optimal time steps based on constraints applied to estimates of the local truncation error. Methods are derived for both error estimation and error control, each of which potentially impacts the stability of the scheme and the global accuracy of the solution. Asymptotic stability and convergence of the recommended time steps are investigated theoretically and demonstrated numerically to identify optimal realizations of the method. This adaptive time stepping scheme requires no solution evaluations or operator inversions beyond those already performed in the adaption-free solution and requires no modifications to the numerical solution algorithm. As such, this adaptivity scheme can be easily implemented in virtually any reactor physics simulation code based on a backward difference discretization of transient neutronics. (C) 2018 Elsevier Ltd. All rights reserved.