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©2012 Civil-Comp Ltd |
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L. Barbié1,2, I. Ramière1 and F. Lebon2
1Nuclear Energy Division, Fuel Study Department, Fuel Simulation Laboratory, French Atomic Commission, Saint-Paul-lez-Durance, France
2Mechanics and Acoustics Laboratory, French National Center for Scientific Research, UPR 7051, Aix-Marseille University, Centrale Marseille, France
Keywords: adaptive mesh refinement, nested local grids, uniform non-data-fitted meshes, local defect correction, a posteriori error estimation, nonlinear solids mechanics, Norton creep, pellet-cladding interaction.
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reference
In this paper, an adaptive mesh refinement (AMR) method, called the
local defect correction (LDC)
technique [1] is applied to solids mechanics with the
objective of conducting reliable nonlinear studies within acceptable
computational times and memory space. This method, devoted to localised
phenomena simulation, has stood the test of time in fluid mechanics
but is almost unused in other fields of physics. However, as no
theoretical reason seems to justify this restriction, it appears
worthwhile to extend this approach to solids mechanics. The LDC method
consists of
recursively generating local nested sub-grids with finer and finer
discretisation steps from an initial coarse grid. An iterative process
based on prolongation and
restriction operators is performed to link the solutions from each
grid. As the meshes are no longer data-fitted the theoretical
convergence rate is limited. Nevertheless, this limitation appears
also in much industrial software that avoids the remeshing technique with the objective of saving CPU time.
A Zienkiewicz and Zhu a posteriori error estimator
[2] is used to automatically detect the local zones
to refine.
The test case of this study comes from an industrial
situation: the pellet-cladding interaction in pressurised water
reactors [3]. During the irradiation, the fuel pellet
swells and the cladding creeps and shrinks that induces contact. This
phenomenon is very localised. Complete three-dimensional simulations are currently
impossible as a result of the required unstructured and irregular mesh. The
LDC approach appears to be well suited to overcome this kind of issue.
Our simulations focus on the cladding response. The
contact with the pellet is represented by a discontinuous pressure on
its internal radius. As this test case is not an academic problem but an
industrial one, analytical solutions are generally not available.
Our approach is first validated by using a linear behaviour,
comparing two and three dimensional local dect correction (LDC) simulations with solutions obtained using
very fine global meshes. The expected results are obtained: the final
corrected coarse solution is as precise as the solution computed on a
unique uniform mesh having a discretisation step equal to the local
finest grid one.
The LDC approach is also compared with a classical finite element
resolution. Using the LDC solver allows CPU time and memory space to be saved.
Moreover, this approach is extended to nonlinear behaviour and
particularly creep behaviour. The conclusions obtained in the linear
validation study are still valid.
- 1
- W. Hackbusch, "Local Defect Correction Method and Domain Decomposition Techniques", Computing Suppl., Springer-Verlag, 5, 89-113, 1984.
- 2
- O. Zienkiewicz, J. Zhu, "A simple error estimator and adaptive procedure for practical engineering analysis", International Journal for Numerical Methods in Engineering, 24, 337-357, 1987.
- 3
- B. Michel, J. Sercombe, G. Thouvenin, R. Chatelet, "3D fuel cracking modelling in pellet cladding mechanical interaction", Engineering Fracture Mechanics, 75, 3581-3598, 2008.
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