Extension of the Discrete-Ordinates Transport Solver IDT to Regular Two-Dimensional Triangular Meshes

In this work, the Integro-Differential Transport solver (IDT), which is one of the transport solvers available in the APOLLO3(R) lattice code, has been extended to handle 2D unstructured meshes. In particular, the previously implemented method of short characteristics (MoSC) used to solve for the spatial variable in the framework of an SN approach has been extended to triangular cells which represent the natural discretization for calculating the hexagonal lattices present in fast reactors. The coefficients of the collision-probability matrices have been evaluated by means of a split-cell algorithm, specialized for dealing with different orientations of the triangle with respect to each discrete ordinate of the SN sweeping. A new sweeping routine for unstructured meshes has been added to IDT. The correct implementation of the method and its robustness with respect to the skewness and the optical thickness of the triangle has been verified. The method of manufactured solutions has been employed to obtain a numerical estimate of the spatial convergence order of the method. The same version of the MoSC has then been implemented in MINARET, another solver available in APOLLO3(R). Finally, the modified IDT applied to an unstructured mesh for the C5G7 benchmark has been successfully benchmarked against MC calculations, and the modified MINARET has been applied to a neutron transport calculation for the RJH research reactor

A PERTURBATIONAL APPROACH TO OBTAIN HIGH ACCURACY WAVELENGTH, APPLIED TO THE SUPERSTRUCTURE CODE

A perturbational method for improving calculated energy levels of atomic elements (Z ≤ 30) at different ionization stages is presented. The method uses as a starting point the SUPERSTRUCTURE code developed at the University College London and uses scaled Thomas-Fermi potentials. The perturbation theory is applied up to the second order energy correction and introduces the contribution of the complete basis, including continuum states of the unperturbed hamiltonian. As an illustration the method is applied to the determination of some energy terms of the He-like oxygen ion

Component mode synthesis methods for 3-D heterogeneous core calculations applied to the mixed-dual finite element solver MINOS

International audienceThis paper describes a new technique for determining the pin power in heterogeneous 3D calculations. It is based on a domain decomposition with overlapping subdomains and a component mode synthesis technique for the global flux determination. Local basis functions are used to span a discrete space that allows fundamental global mode approximation through a Galerkin technique. Two approaches are given to obtain these local basis functions in the first one (Component Mode Synthesis method), the first few spatial eigenfunctions are computed on each subdomain, using periodic boundary conditions. In the second one (Factorized Component Mode Synthesis method), only the fundamental mode is computed, and we use a factorization principle for the flux in order to replace the higher order eigenmodes. These different local spatial functions are extended to the global domain by defining them as zero outside the subdomain. These methods are well-fitted for heterogeneous core calculations because the spatial interface modes are taken into account in the domain decomposition. Although these methods could be applied to higher order angular approximations - particularly easily to a approximation - the numerical results we provide are obtained using a diffusion model. We show the methods- accuracy for reactor cores loaded with UOX and MOX assemblies, for which standard reconstruction techniques are known to perform poorly. Furthermore, we show that our methods are highly and easily parallelizable

Coarse Mesh Rebalance Acceleration Applied to an Iterative Domain Decomposition Method on Unstructured Mesh

International audienceAn iterative domain decomposition method (DDM) is implemented inside the APOLLO3 Sntransport core solver MINARET. Based on a block-Jacobi algorithm, the method inherently suffers a convergencepenalty in terms of both computing time and number of iterations. An acceleration method has to bedeveloped in order to overcome this difficulty. This paper investigates a nonlinear coarse mesh rebalance (CMR)method that favors the way information propagates through the core when domain decomposition is used. Thefundamental idea involves updating each subdomain boundary condition thanks to a core-sized low-ordercalculation on a coarse spatial mesh. The numerical convergence is sped up. Performances are meeting theexpectations since the CMR acceleration systematically succeeds in overbalancing the domain decompositionadditional cost. The aim of such a DDM + CMR algorithm is eventually to introduce more parallelism whensolving the spatial transport equation. Nevertheless, parallel computing is not addressed in this paper

Performance study of a parallel domain decomposition method

International audienceThis paper studies the influence of various parameters, in order to improve the performances of a parallel Domain Decomposition Method ($aka$ DDM). If introducing more parallelism represents an opportunity to heighten the performance of deterministic schemes, substantial modifications of their architecture are required. In this context, DDM has been implemented into the Apollo3 multigroup $S_n$ solver, Minaret. The fundamental idea involves splitting a large boundary value problem into several $independent$ subproblems, that can be computed in parallel.Two $DDM$ algorithms are considered. The first one solves a one-group problem per subdomain. The second one is a multigroup block-Jacobi algorithm. To improve performances of these DDM,various parallelism strategies are implemented and compared, depending on the internal structure of the DDM algorithm, the technology chosen (MPI or OpenMP), and the variable parallelized (angular direction or subdomain). Based on these considerations, an efficient $hybrid$ parallelism,suitable for $HPC$ is built a parallel multigroup Jacobi iteration algorithm, using a two layerMPI/OpenMP architecture, gives the best performances for the reactor configuration studied

A domain decomposition method in APOLLO3R^R solver, MINARET

International audienceThe aim of this paper is to present the last developments made on Domain Decomposition Methodinside the APOLLO3$^R$ core solver, MINARET. The fundamental idea consists in splitting a large boundaryvalue problem into several similar but smaller ones. Since each sub-problem can be solved independently,the Domain Decomposition Method is a natural candidate to introduce more parallel computing intodeterministic schemes. Yet, the real originality of this work does not rest on the well-tried DomainDecomposition Method, but in its implementation inside MINARET. The first validation elements show aperfect equivalence between the reference and the Domain Decomposition schemes, in terms of both$k_{eff}$ and flux mapping. These first results are obtained without any parallelization or acceleration.Nevertheless, the “relatively“ low increase of computation time due to Domain Decomposition is veryencouraging for future performances. So much that one can hope to greatly increase the precisionwithout any major time impact for users. At last, the unstructured space meshing used in MINARET willeventually be improved by adding an optional non conformal map between subdomains. This associationwill make of the new scheme an efficient tool, able to deal with the large variety of geometries offered bynuclear core concepts

Deterministic model of PWR fast fluence for uncertainity propagations with the code APOLLO3

International audienceThe fast neutron fluence and the corresponding uncertainty are important parameters for reactor pressure vessel life time. This article presents one model, under development at CEA (Commissariat a l-Energie Atomique et aux Energies Alternatives), to carry out with the deterministic code APOLLO3$^R$ uncertainty calculations of the fast fluence for PWR irradiation surveillance. All calculations are made by MINARET, a 3D-SN solver of the APOLLO3 code which uses the discontinuous Galerkin finite elements approximation. The spatial mesh is unstructured and the transport calculations are parallelized with respect to the angular directions. In this numerical scheme, the multigroup cross-sections are sub-group self-shielded and collapsed over a dedicated energy mesh optimized by the Adaptive Energy Mesh Constructor (AEMC). Results from this model are encouraging with respect to the Monte Carlo reference TRIPOLI-4$^R$. The integral of the flux over 1 MeV in the locations of interest (surveillance capsule and vessel) is calculated in less than 20 minutes with an error lower than 1percent. Some examples of uncertainty calculations associated to design parameters in which the MINARET solver is coupled to the CEA uncertainty and sensitivity platform URANIE are also provided

SATELLITE LINES OF NEON-LIKE RESONANCE LINES, FOR 17<Z<48

The dielectronic satellite lines of the neon-like resonance lines 1s22s22p53d - 1s22s22p6 have been observed in the spectra obtained during the Limeil X-ray Laser experiments under collisional dense plasma conditions (102