Keywords: heat and moisture transport, domain decomposition methods, Schur complement, parallel computing.

Many nuclear power plants in Europe are approaching the end of their design life. The high costs of decommissioning and replacement of the existing plants has made the prolongation of their service a viable option. As a result of this, the assessment of the effects of ageing in safety related concrete structures in nuclear power plants has recently become an important issue.

There are many types of reactor vessels but this contribution deals with prestressed concrete reactor vessels with inner steel liner, which are used in the United Kingdom. This paper describes numerical simulations of the ageing processes by using domain decomposition methods on parallel computers.

During their life the reactor vessels undergo a history comprising gravity loads, prestressing (which decreases with time), an internal pressurisation proof test and a series thermal and pressure cycles. These influences cause changes in the characteristics of the vessel with age.

The effects of the ageing processes on the properties of the vessel were assessed by a combination of mechanical, heat and moisture transport and coupled thermo-hygro-mechanical analyses. The mechanical analysis comprises a creep analysis based on B3 creep model and a limit state analysis which starts from values obtained from either pure mechanical or coupled thermo-hygro-mechanical analysis.

All simulations covered a period of more than thirty years. The time step in the computations was set up with respect to the gradients of different variables, such as stress and temperature: from two hours during intensive heating of the vessel to one day during the steady-state phases. As a result, each analysis was performed with more than 12,500 time steps. Furthermore, due to the highly nonlinear nature of the problem, the Newton-Raphson method was used and several iterations were performed to reach the equilibrium in each time step.

Considering the number of steps and the relatively detailed meshes required to capture the behaviour of the structure (34,000 DOF), it is clear that the assessment of the ageing processes in reactor vessels requires a significant computational power. Parallel processing offers a suitable tool for this type of simulations. All algorithms used in the analyses were coded with respect to parallelization, using the domain decomposition concept of non-overlapping subdomains. Due to non-symmetry of the conductivity and capacity matrices, the Schur complement method was used and reduced (coarse) problem was solved by either direct (LU factorization) or iterative method (bi-conjugate gradient method).

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