A COMPARISON OF THERMOMECHANICS COUPLING STRATEGIE Page: 3 of 10
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22"a Conference on Structural Mechanics in Reactor Technology
San Francisco, California, USA - August 18-23, 2013
there is strong two-way feedback between the physics, that approach can have an unacceptably slow
convergence rate and is more likely to encounter convergence difficulty.
In tight coupling solution methods, a single system of equations is assembled and solved for the
full set of coupled physics. The nonlinear iterations operate on the full system of equations
simultaneously, taking into account the interactions between the equations for the coupled physics in each
iteration. In cases where there is strong coupling between the physics, this approach can have faster
convergence rates than loose coupling. The primary disadvantage of this approach is that it necessitates
tighter coordination between the codes to solve the individual physics.
In thermomechanical problems, in the absence of evolving contact between components, the
coupling between the heat conduction and solid mechanics equations is often primarily one-way. The
temperatures obtained from the heat conduction equations cause thermal strains, which result in
displacement of the mechanical model. These displacements typically have a negligible effect on the
thermal model, and such problems can be readily solved using loose coupling strategies, or even by
transferring data from a thermal code to a solid mechanics code and completely neglecting the effect of
the mechanical solution on the thermal solution.
Introducing evolving mechanical and thermal contact to thermomechanical problems transforms
them from being essentially one-way coupled problems to strongly two-way coupled problems. This is
because the conductance across gaps between adjacent bodies is highly dependent on the distance
between those bodies, which is a function of the solid mechanics equations. Because the fuel system used
in LWRs relies on heat transfer across the evolving fuel/cladding gap, the ability to solve the strongly
coupled thermal and mechanical equations in the presence of evolving contact conditions is critical for a
successful fuel performance modeling code.
Similar work presented by Novascone et al. (2013) was primarily focused on two simple
thermomechanics problems with thermal and mechanical contact. In this paper, we present realistic
simulations of a single LWR fuel pin for both tightly coupled and loosely coupled strategies. The
difficultly in obtaining converged solutions of fuel-clad interaction problems is considerable, mainly due
to the complexity of the fuel and clad material models and the degrading thermal conductance of the gap
due to fission gas release.
BISON FUEL PERFORMANCE CODE
The Jacobian-Free Newton Krylov (Knoll and Keyes, 2004) method has emerged as a powerful
technique to facilitate the tightly coupled solution of multiphysics problems. As its name implies, this
technique uses Newton's method to simultaneously solve the full system of nonlinear equations,
including all coupling terms. In contrast to the traditional Newton's method, however, the system tangent
matrix is not constructed in JFNK. Instead, a Krylov method is used to perform linear iterations to form
the search direction vector that is used in each nonlinear iteration. Krylov methods only require the action
of the tangent matrix on a solution vector, and do not require the tangent matrix to be constructed. This
facilitates multiphysics coupling because it enables the tightly coupled solution of the coupled equations
without constructing the full system tangent matrix, which can be very difficult. An approximation of the
coupled system matrix can be used as a preconditioner for the Krylov method, but it does not need to be
the exact matrix.
The Idaho National Laboratory (INL) is developing a next-generation nuclear fuel performance
analysis code called BISON (Williamson et al. 2012). BISON is built on INLs Multiphysics Object-
Oriented Simulation Environment (MOOSE) (Gaston et al. 2009), which is a massively parallel finite
element-based framework used to solve general systems of coupled nonlinear partial differential
equations. For the reasons outlined above, BISON and MOOSE use JFNK to solve systems of equations
in a tightly coupled manner.
BISON solves tightly coupled systems of partial differential equations for the physics involved in
nuclear fuel, which can include energy, species diffusion, and momentum conservation. BISON uses the
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Novascone, S. R.; Andrs, D.; Spencer, B. W. & Ha, J. D. A COMPARISON OF THERMOMECHANICS COUPLING STRATEGIE, article, August 1, 2013; [Idaho Falls, Idaho]. (https://digital.library.unt.edu/ark:/67531/metadc863298/m1/3/: accessed April 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.