1 IL SISTEMA DI CALCOLO MODULARE ERANOS (EUROPEAN REACTOR ANALYSIS OPTIMIZED SYSTEM) CORE CALCULATIONS

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4 CORE and GEOMETRY The whole core can be described. That covers the disposition of the sub- assemblies, the nature and geometry of the blanket, the description of the control rods, special elements… To be complete, you shall define the geometry. A calculation can be 1D, 2D or 3D 1D: spherical, cylindrical or plane 2D: XY, Hexagonal, RZ or Rθ 3D: XYZ or Hexagonal-Z The core creation step is used only for 2D and 3D geometries. It is optional, and all can be described in a geometry creation (warning: some ERANOS modules may require a core SET in their input data). When both core and geometry creations are used, the core description tells where the subassemblies of different types may be placed, and the geometry description where they are actually placed and what are the control rod positions and the boundary conditions

5 DIFFUSION and TRANSPORT Solution using the Finite Differences Method The DIFFUSION group solves the diffusion problem with a finite differences method. Every geometry mentioned above is available. Basically you can calculate the flux, but many alternatives are available like adjoint calculations or calculations with an external source. The BISTRO (BI-dimensional Sn TRansport Optimisé ) group solves the transport problem (direct or adjoint) with the SN method. For the space variable, it also is a finite differences method. The available geometries are cylindrical, spherical and plane 1D, XY and RZ. With BISTRO you can also perform perturbation, sensitivity and uncertainty calculations, but you cannot perform kinetics calculations. VARIANT: Nodal Method The TGV/VARIANT group solves the transport (or diffusion) problem with a nodal method. The available geometries are XY or Hexagonal in 2D and XYZ or Hexagonal-Z in 3D. With VARIANT you can also perform kinetics and perturbation calculations.

6 The Diffusion Modules For any geometry, the DIFFUSION group is made with several modules, and produces several SETs. The breaking-up of the diffusion calculation in functions leads to define several functions, with several corresponding modules. The specific functions are: The geometry definition (hexagonal 2d or 3d or rectangular 1d,2d,3d). The calculation of the coefficients of the diffusion matrices, which are the same for the direct, adjoint, homogeneous or inhomogeneous problems. The definition of the solving method, and the calculation of its parameters. The definition of the external sources for the inhomogeneous problem. The discretisation of those sources on the calculation geometry. The processing of the diffusion iterations. The editing of every SET created or used by those functions

7 The Diffusion Modules The SETS are: GEOMETRY Hexagonal or rectangular Geometry for calculations. MACRO Macroscopic cross-sections. COEFFICIENTS The coefficients of the matrices made discrete on the calculation geometry. EXTERNAL SOURCE COEFFICIENTS The external source coefficients made discrete on the calculation geometry. METHOD The selected solving method and its associated parameters. FLUX The flux vector which is the solution of a diffusion problem.

8 The Transport Modules The specific functions are: The geometry definition (rectangular 1d or 2d). The calculation of the coefficients of the transport matrices, which are the same for the direct, adjoint, homogeneous or inhomogeneous problems, and which may be executed by the function which calculates the diffusion coefficients. The definition of the solving method, and the calculation of its parameters. The definition of the external sources for the inhomogeneous problem. The discretisation of those sources on the calculation geometry. The SN method specific functions: The definition of the selected weights and cosines, The processing of the transport iterations. The editing of every SET created or used by those functions.

9 The Transport Modules Every necessary diffusion function must be used here because the diffusion is used to speed up the transport. The SETS are: GEOMETRY Hexagonal or rectangular geometry. MACRO Macroscopic cross-sections. COEFFICIENTS The coefficients of the matrices made discrete on the calculation geometry. EXTERNAL SOURCE METHOD The selected solving method and its associated parameters. COSINES AND WEIGHTS Weights and cosineus of the angular directions. SCALAR FLUX The external source coefficients made discrete on the calculation geometry. The scalar flux vector which is the solution of a transport problem. ANGULAR FLUX The angular flux vector which is the solution of a transport problem.

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23 Correction de Maillage Spatial