 
Summary: A Generalized Adjoint Framework for Sensitivity and Global Error
Estimation in TimeDependent Nuclear Reactor Simulations 1
H. F. Striplinga,
, M. Anitescub
, M. L. Adamsa
aNuclear Engineering Department, Texas A&M University, 3133 TAMU, College Station, TX 778433133
bArgonne National Laboratory, Mathematics and Computer Science Division, 9700 S Cass Avenue, Argonne, IL 60439
Abstract
We develop a general framework for computing the adjoint variable to nuclear engineering problems gov
erned by a set of differentialalgebraic equations (DAEs). The nuclear engineering community has a rich
history of developing and applying adjoints for sensitivity calculations; many such formulations, however,
are specific to a certain set of equations, variables, or solution techniques. Any change or addition to the
physics model would require a reformulation of the adjoint problem and substantial difficulties in its soft
ware implementation. In this work we propose an abstract framework that allows for the modification and
expansion of the governing equations, leverages the existing theory of adjoint formulation for DAEs, and
results in adjoint equations that can be used to efficiently compute sensitivities for parametric uncertainty
quantification. Moreover, as we justify theoretically and demonstrate numerically, the same framework can
be used to estimate global time discretization error.
We first motivate the framework and show that the coupled Bateman and transport equations, which
govern the timedependent neutronic behavior of a nuclear reactor, may be formulated as a DAE system
