| 1. |
- Dufek, Jan, 1978-
(författare)
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Development of New Monte Carlo Methods in Reactor Physics : Criticality, Non-Linear Steady-State and Burnup Problems
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The Monte Carlo method is, practically, the only approach capable of giving detail insight into complex neutron transport problems. In reactor physics, the method has been used mainly for determining the keff in criticality calculations. In the last decade, the continuously growing computer performance has allowed to apply the Monte Carlo method also on simple burnup simulations of nuclear systems. Nevertheless, due to its extensive computational demands the Monte Carlo method is still not used as commonly as deterministic methods. One of the reasons for the large computational demands of Monte Carlo criticality calculations is the necessity to carry out a number of inactive cycles to converge the fission source. This thesis presents a new concept of fission matrix based Monte Carlo criticality calculations where inactive cycles are not required. It is shown that the fission matrix is not sensitive to the errors in the fission source, and can be thus calculated by a Monte Carlo calculation without inactive cycles. All required results, including keff, are then derived via the final fission matrix. The confidence interval for the estimated keff can be conservatively derived from the variance in the fission matrix. This was confirmed by numerical test calculations of Whitesides's ``keff of the world problem'' model where other Monte Carlo methods fail to estimate the confidence interval correctly unless a large number of inactive cycles is simulated. Another problem is that the existing Monte Carlo criticality codes are not well shaped for parallel computations; they cannot fully utilise the processing power of modern multi-processor computers and computer clusters. This thesis presents a new parallel computing scheme for Monte Carlo criticality calculations based on the fission matrix. The fission matrix is combined over a number of independent parallel simulations, and the final results are derived by means of the fission matrix. This scheme allows for a practically ideal parallel scaling since no communication among the parallel simulations is required, and no inactive cycles need to be simulated. When the Monte Carlo criticality calculations are sufficiently fast, they will be more commonly applied on complex reactor physics problems, like non-linear steady-state calculations and fuel cycle calculations. This thesis develops an efficient method that introduces thermal-hydraulic and other feedbacks into the numerical model of a power reactor, allowing to carry out a non-linear Monte Carlo analysis of the reactor with steady-state core conditions. The thesis also shows that the major existing Monte Carlo burnup codes use unstable algorithms for coupling the neutronic and burnup calculations; therefore, they cannot be used for fuel cycle calculations. Nevertheless, stable coupling algorithms are known and can be implemented into the future Monte Carlo burnup codes.
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| 2. |
- Chan, Yi Meng, et al.
(författare)
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A deep-learning representation of multi-group cross sections in lattice calculations
- 2024
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Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 195
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Tidskriftsartikel (refereegranskat)abstract
- To compute few-group nodal cross sections, lattice codes must first generate multi-group cross sections using continuous energy cross-section libraries for each material in each fuel cell. Since the processing cost is significant, we propose representing the multi-group cross sections during lattice calculations using a pre-trained deep-learning-based model. The model utilizes a combination of Principal Component Analysis (PCA) and fully connected Neural Networks (NN). The model is specifically designed to manage extensive multi-group cross-section data sets, which contain data for several dozen nuclides and encompass more than 50 energy groups. Our testing of the trained model on a PWR assembly with a realistic boron letdown curve revealed an average relative error of around 0.1% for both fission and total macroscopic cross sections. The average time required for the model to generate the cross sections was approximately 0.01% of the time needed to execute the cross-section processing module.
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| 3. |
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| 4. |
- Dufek, Jan, 1978
(författare)
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Building the nodal nuclear data dependences in a many-dimensional state-variable space
- 2011
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Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 38:7, s. 1569-1577
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Tidskriftsartikel (refereegranskat)abstract
- We present new methods for building the polynomial-regression based nodal nuclear data models. Thedata models can reflect dependences on a large number of state variables, and they can consider varioushistory effects. Suitable multivariate polynomials that approximate the nodal data dependences are identifiedefficiently in an iterative manner. The history effects are analysed using a new sampling scheme forlattice calculations where the traditional base burnup and branch calculations are replaced by a largenumber of diverse burnup histories. The total number of lattice calculations is controlled so that the datamodels are built to a required accuracy.
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| 5. |
- Dufek, Jan, 1978-
(författare)
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Complex models of nodal nuclear data
- 2011
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Ingår i: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011). - 9788563688002
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Konferensbidrag (refereegranskat)abstract
- During the core simulations, nuclear data are required at various nodal thermal-hydraulic and fuel burnup conditions. The nodal data are also partially affected by thermal-hydraulic and fuel burnup conditions in surrounding nodes as these change the neutron energy spectrum in the node. Therefore, the nodal data are functions of many parameters (state variables), and the more state variables are considered by the nodal data models the more accurate and flexible the models get. The existing table and polynomial regressionmodels, however, cannot reflect the data dependences on many state variables. As for the table models, the number of mesh points (and necessary lattice calculations) grows exponentially with the number of variables. As for the polynomial regression models, the number of possible multivariate polynomials exceeds the limits of existing selection algorithms that should identify a few dozens of the most important polynomials. Also, the standard scheme of lattice calculations is not convenient for modelling the data dependences on various burnup conditions since it performs only a single or few burnup calculations at fixed nominal conditions. We suggest a new efficient algorithm for selecting the most important multivariate polynomials for the polynomial regression models so that dependences on many state variables can be considered. We also present a new scheme for lattice calculations where a large number of burnup histories are accomplished at varied nodal conditions. The number of lattice calculations being performed and the number of polynomials being analysed are controlled and minimised while building the nodal data models of a required accuracy.
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| 6. |
- Dufek, Jan, 1978-, et al.
(författare)
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Monte Carlo criticality calculations accelerated by a growing neutron population
- 2016
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Ingår i: Annals of Nuclear Energy. - : Elsevier. - 0306-4549 .- 1873-2100. ; 94, s. 16-21
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Tidskriftsartikel (refereegranskat)abstract
- We propose a fission source convergence acceleration method for Monte Carlo criticality simulation. As the efficiency of Monte Carlo criticality simulations is sensitive to the selected neutron population size, the method attempts to achieve the acceleration via on-the-fly control of the neutron population size. The neutron population size is gradually increased over successive criticality cycles so that the fission source bias amounts to a specific fraction of the total error in the cumulative fission source. An optimal setting then gives a reasonably small neutron population size, allowing for an efficient source iteration; at the same time the neutron population size is chosen large enough to ensure a sufficiently small source bias, such that does not limit accuracy of the simulation.
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| 7. |
- Dufek, Jan, 1978-, et al.
(författare)
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Optimal time step length and statistics in Monte Carlo burnup simulations
- 2020
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Ingår i: Annals of Nuclear Energy. - : Elsevier. - 0306-4549 .- 1873-2100. ; 139
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Tidskriftsartikel (refereegranskat)abstract
- Monte Carlo burnup simulations continue to be seen as computationally very expensive numerical routines despite recent developments of associated methods. Here, we suggest a way of improving the computing efficiency via optimisation of the length of the time steps and the number of neutron histories that are simulated at each Monte Carlo criticality run. So far, users of Monte Carlo burnup codes have been required to set these parameters at will; however, an inadequate choice of these free parameters can severely worsen the computing efficiency. We have tested a large number of combinations of the free parameters on a simplified and fast solver, and we have observed that the computing efficiency was maximized when the computing cost of all Monte Carlo neutron transport calculations (summed over all time steps) was approximately comparable to costs of other procedures (all depletion simulations, the loading and processing of neutron cross sections, etc.). In this technical note, we demonstrate these results, and we also derive a simple theoretical model of the convergence of Monte Carlo burnup simulations that conforms to these numerical results. Here, we also suggest a straightforward way to automatise the selection of the optimal values of the free parameters for Monte Carlo burnup simulations.
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| 8. |
- Dufek, Jan, 1978-, et al.
(författare)
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Optimisation of Monte Carlo burnup simulations
- 2020
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Ingår i: International Conference on Physics of Reactors. - : EDP Sciences. ; , s. 804-810
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Konferensbidrag (refereegranskat)abstract
- We show here that computing efficiency of Monte Carlo burnup simulations depends on chosen values of certain free parameters, such as the length of the time steps and the number of neutron histories simulated at each Monte Carlo criticality run. The efficiency can thus be improved by optimising these parameters. We have set up a simple numerical model that made it possible for us to test a large number of combinations of the free parameters, and suggest a way to optimise their selection.
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| 9. |
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| 10. |
- Hoogenboom, J. Eduard, et al.
(författare)
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Optimised Iteration in Coupled Monte Carlo - Thermal-Hydraulics Calculations
- 2016
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Ingår i: SNA + MC 2013 - JOINT INTERNATIONAL CONFERENCE ON SUPERCOMPUTING IN NUCLEAR APPLICATIONS + MONTE CARLO. - Les Ulis, France : E D P SCIENCES.
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Konferensbidrag (refereegranskat)abstract
- This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration method are also tested and it is concluded that the presented iteration method is near optimal.
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| 11. |
- Ignas, Mickus
(författare)
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Response Matrix Reloaded : for Monte Carlo Simulations in Reactor Physics
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis investigates Monte Carlo methods applied to criticality and time-dependent problems in reactor physics. Due to their accuracy and flexibility, Monte Carlo methods are considered as a “gold standard” in reactor physics calculations. However, the benefits come at a significant computing cost. Despite the continuous rise in easily accessible computing power, a brute-force Monte Carlo calculation of some problems is still beyond the reach of routine reactor physics analyses. The two papers on which this thesis is based try to address the computing cost issue, by proposing methods for performing Monte Carlo reactor physics calculations more efficiently. The first method addresses the efficiency of the widely-used k-eigenvalue Monte Carlo criticality calculations. It suggests, that the calculation efficiency can be increased through a gradual increase of the neutron population size simulated during each criticality cycle, and proposes a way to determine the optimal neutron population size. The second method addresses the application of Monte Carlo calculations to reactor transient problems. While reactor transient calculations can, in principle, be performed using only Monte Carlo methods, such calculations take multiple thousands of CPU hours for calculating several seconds of a transient. The proposed method offers a middle-ground approach, using a hybrid stochastic-deterministic scheme based on the response matrix formalism. Previously, the response matrix formalism was mainly considered for steady-state problems, with limited application to time-dependent problems. This thesis proposes a novel way of using information from Monte Carlo criticality calculations for solving time-dependent problems via the response matrix.
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| 12. |
- Mickus, Ignas, et al.
(författare)
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Application of response matrix method to transient simulations of nuclear systems
- 2020
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Ingår i: International Conference on Physics of Reactors. - : EDP Sciences. ; , s. 786-793
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Konferensbidrag (refereegranskat)abstract
- Until recently, reactor transient problems were exclusively solved by approximate deterministic methods. The increase in available computing power made it feasible to approach the transient analyses with time-dependent Monte Carlo methods. These methods offer the first-principle solution to the space-time evolution of reactor power by explicitly tracking prompt neutrons, precursors of delayed neutrons and delayed neutrons in time and space. Nevertheless, a very significant computing cost is associated with such methods. The general benefits of the Monte Carlo approach may be retained at a reduced computing cost by applying a hybrid stochastic-deterministic computing scheme. Among such schemes are those based on the fission matrix and the response matrix formalisms. These schemes aim at estimating a variant of the Greens function during a Monte Carlo transport calculation, which is later used to formulate a deterministic approach to solving a space-time dependent problem. In this contribution, we provide an overview of the time-dependent response matrix method, which describes a system by a set of response functions. We have recently suggested an approach where the functions are determined during a Monte Carlo criticality calculation and are then used to deterministically solve the space-time behaviour of the system. Here, we compare the time-dependent response matrix solution with the transient fission matrix and the time-dependent Monte Carlo solutions for a control rod movement problem in a mini-core reactor geometry. The response matrix formalism results in a set of loosely connected equations which offers favourable scaling properties compared to the methods based on the fission matrix formalism.
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| 13. |
- Mickus, Ignas, et al.
(författare)
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Does neutron clustering affect tally errors in Monte Carlo criticality calculations?
- 2021
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Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 155
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Tidskriftsartikel (refereegranskat)abstract
- Monte Carlo criticality calculations of large, loosely-coupled problems are long known to suffer from slow convergence of the tally errors due to cycle-to-cycle fission source correlations. In several recent studies, it was suggested that these correlations could be possibly attributed to the neutron clustering phenomenon that is visible in calculations with a small number of neutrons per iteration cycle (batch size). Nevertheless, other studies have also shown the error convergence rate in such loosely-coupled problems to be batch size-independent during active criticality cycles. Here, we aim to address this inconsistency by studying the error convergence in a large number of test calculations, varying the neutron batch size from small to large. In our tests, we have observed that the presence of visible neutron clusters does not increase the cycle-to-cycle fission source correlations and does not worsen the convergence rate of the tally errors.
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| 14. |
- Mickus, Ignas, et al.
(författare)
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Optimal neutron population growth in accelerated Monte Carlo criticality calculations
- 2018
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Ingår i: Annals of Nuclear Energy. - : Elsevier. - 0306-4549 .- 1873-2100. ; 117, s. 297-304
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Tidskriftsartikel (refereegranskat)abstract
- We present a source convergence acceleration method for Monte Carlo criticality calculations. The method gradually increases the neutron population size over the successive inactive as well as active criticality cycles. This helps to iterate the fission source faster at the beginning of the simulation where the source may contain large errors coming from the initial cycle; and, as the neutron population size grows over the cycles, the bias in the source gets reduced. Unlike previously suggested acceleration methods that aim at optimisation of the neutron population size, the new method does not have any significant computing overhead, and moreover it can be easily implemented into existing Monte Carlo criticality codes. The effectiveness of the method is demonstrated on a number of PWR full-core criticality calculations using a modified SERPENT 2 code.
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| 15. |
- Mickus, Ignas, et al.
(författare)
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Stochastic-deterministic response matrix method for reactor transients
- 2020
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Ingår i: Annals of Nuclear Energy. - : Elsevier. - 0306-4549 .- 1873-2100. ; 140, s. 107103-
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Tidskriftsartikel (refereegranskat)abstract
- Presented is a stochastic-deterministic, response matrix method for transient analyses of nuclear systems. The method is based on the response matrix formalism, which describes a system by a set of response functions. We propose an approach in which these response functions are computed during a set of Monte Carlo criticality calculations and are later used to formulate a deterministic set of equations for solving a space-time dependent problem. Application of the response matrix formalism results in a set of loosely connected equations, which leads to a favourable linear scaling of the problem. The method offers a simplified approach compared to previously proposed response matrix methods by avoiding phase-space expansions in sets of basis functions. We describe the method starting with the fundamental neutron transport considerations, provide a demonstration on two absorber movement transients in a 3 × 3 assembly PWR mini-core geometry, and compare the solutions against time-dependent Monte Carlo simulations.
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| 16. |
- Mickus, Ignas
(författare)
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Towards Efficient Monte Carlo Calculations in Reactor Physics : Criticality, Kinetics and Burnup Problems
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis presents a compilation of work focused on Monte Carlo crit-icality, kinetics and burnup calculations in reactor physics. Performing suchcalculations usually comes at a high computing cost. Therefore, the main mo-tivation behind the presented work is lowering the computing cost of MonteCarlo calculations. To this end, three new methods for improving the comput-ing efficiency are proposed: a method for neutron population control in MonteCarlo criticality calculations; a hybrid stochastic-deterministic response ma-trix method for reactor kinetics calculations; and an optimisation method forMonte Carlo burnup calculations.The first method gradually increases the neutron population size over thesuccessive cycles in Monte Carlo criticality calculations. This enables fasterfission source iterations at the beginning of a calculation where the sourcemay contain errors from the initial cycle while at the same time preventingthe source bias from dominating the error later in the calculation. The methodis tested on a set of full-core PWR criticality calculations.The second method is based on the response matrix formalism which de-scribes a system by a set of response functions. The response functions arecomputed during Monte Carlo criticality calculations. These functions arethen used in a deterministic set of equations for solving a space-time depen-dent problem. The method is demonstrated on a set of absorber movementtransients in a PWR-type mini-core.The third method sets the time step length and the number of neutronhistories simulated during each time step of Monte Carlo burnup calculationsaccording to the fraction of the computing cost assigned to the depletion solu-tions (and other procedures that are repeatedly executed before starting theactive cycles) and the overall computing cost of a Monte Carlo burnup calcu-lation. Optimal values of this fraction are studied in a set of test calculations.Additionally, numerical tests on tally error convergence in Monte Carlocriticality calculations and stability of Monte Carlo burnup calculations arepresented. The context and the outcomes of the work are summarized inthe main body of the thesis while the details are presented in the appendedpublications.
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| 17. |
- Sanchez-Espinoza, V. H., et al.
(författare)
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The McSAFE project - High-performance Monte Carlo based methods for safety demonstration : From proof of concept to industry applications
- 2020
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Ingår i: International Conference on Physics of Reactors. - : EDP Sciences. ; , s. 943-950
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Konferensbidrag (refereegranskat)abstract
- The increasing use of Monte Carlo methods for core analysis is fostered by the huge and cheap computer power available nowadays e.g. in large HPC. Apart from the classical criticality calculations, the application of Monte Carlo methods for depletion analysis and cross section generation for diffusion and transport core simulators is also expanding. In addition, the development of multi-physics codes by coupling Monte Carlo solvers with thermal hydraulic codes (CFD, subchannel and system thermal hydraulics) to perform full core static core analysis at fuel assembly or pin level has progressed in the last decades. Finally, the extensions of the Monte Carlo codes to describe the behavior of prompt and delay neutrons, control rod movements, etc. has been started some years ago. Recent coupling of dynamic versions of Monte Carlo codes with subchannel codes make possible the analysis of transient e.g. rod ejection accidents and it paves the way for the simulation of any kind of design basis accidents as an alternative option to the use of diffusion and transport based deterministic solvers. The H2020 McSAFE Project is focused on the improvement of methods for depletion considering thermal hydraulic feedbacks, extension of the coupled neutronic/thermal hydraulic codes by the incorporation of a fuel performance solver, the development of dynamic Monte Carlo codes and the development of methods to handle large depletion problems and to reduce the statistical uncertainty. The validation of the multi-physics tools developed within McSAFE will be performed using plant data and unique tests e.g. the SPERT III E REA test. This paper will describe the main developments, solution approaches, and selected results.
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