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The Sodium Reactor Experiment
In February 1957, construction was completed on the Sodium Reactor Experiment (SRE), a sodium-cooled, graphite-moderated reactor with an output of 20 MWt. The design of theSRE had begun three years earlier in 1954, and construction started in April 1955. On April 25, 1957, the reactor reached criticality, and the SRE operated until February 1964.
Alexander Lindsay, Roy Stogner, Derek Gaston, Daniel Schwen, Christopher Matthews, Wen Jiang, Larry K. Aagesen, Robert Carlsen, Fande Kong, Andrew Slaughter, Cody Permann, Richard Martineau
Nuclear Technology | Volume 207 | Number 7 | July 2021 | Pages 905-922
Technical Paper | doi.org/10.1080/00295450.2020.1838877
Articles are hosted by Taylor and Francis Online.
Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.