New Numerical Solution with the Method of Short Characteristics for 2-D Heterogeneous Cartesian Cells in the APOLLO2 Code: Numerical Analysis and Tests

Masiello, Emiliano; Sanchez, Richard; Zmijarevic, Igor

doi:10.13182/nse161-257

Cited by 19 publications

(7 citation statements)

References 12 publications

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“…Following definitions (17) and ( 18) one can notice that in (20), F(u) is independent of u, and is either the boundary flux f or the flux coming from the neighbouring regions of D r . Furthermore, one can sum (19) over all mesh elements to obtain a global formulation. In practice, the local formulation is the one used for implementation purpose, since as described in the section 3.5, the matrices resulting from the discretization are not assembled.…”

Section: The Fully Discretized Problemmentioning

confidence: 99%

Spherical Harmonics and Discontinuous Galerkin Finite Element Methods for the Three-Dimensional Neutron Transport Equation: Application to Core and Lattice Calculation

Assogba

Bourhrara

Zmijarevic

et al. 2023

Nuclear Science and Engineering

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The spherical harmonics or P N method is intended to approximate the neutron angular flux by a linear combination of spherical harmonics of degree at most N . In this work, the P N method is combined with discontinuous Galerkin finite elements method and yield to a full discretization of the multigroup neutron transport equation. The employed method is able to handle all geometries describing the fuel elements without any simplification nor homogenisation. Moreover the use of a matrix assembly-free method avoids building large sparse matrices, which enables to produce high-order solutions in small computational time and less storage usage. The resulting transport solver called NYMO has a wide range of applications: it can be used for a core calculation as well as for a precise 281-groups lattice calculation accounting anisotropic scattering. To assess the accuracy of this numerical scheme, it was applied to 3D reactor core and fuel assembly calculations. These calculations point out that the proposed P N -DG method is capable of producing precise solutions while the developed solver is able to handle complex 3D core and assemblies geometries.

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Section: The Fully Discretized Problemmentioning

confidence: 99%

Spherical Harmonics and Discontinuous Galerkin Finite Element Methods for the Three-Dimensional Neutron Transport Equation: Application to Core and Lattice Calculation

Assogba

Bourhrara

Zmijarevic

et al. 2023

Nuclear Science and Engineering

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“…The IDT solver is a discrete-ordinates neutral-particle transport code based on XYZ geometry. In the past years, IDT has been extended to Heterogeneous Cartesian Cells (HCC) to model fuel pins of nuclear reactor in their exact geometries without need of spatial homogenization, [6]. The HCC model has proven accurate results while saving the number of spatial meshes and, thus, computational time and memory.…”

Section: Linear Short Characteristics and Heterogeneous Cartesian Cel...mentioning

confidence: 99%

“…If we restrict our interest to a single HCC we can specialize Eq. (6). Let us use the following indexes: α, β, γ, ... : indexes of the regions within the HCC, s, s : local boundary surface mesh indexes of the HCC, S ± (Ω d ) : set of the outgoing/incoming local surface indexes with respect to the direction Ω d , t : trajectory index, T (Ω d ) : set of indexes of all the trajectories associated to a given direction Ω d for a given HCC geometrical pattern, T α (Ω d ) : set of indexes of trajectories intersecting the region α of the HCC, T s (Ω) : set of indexes of trajectories intersecting the boundary surface s of the HCC, i, j, k : indexes of the chords of a trajectory, I t (Ω d ) : set of indexes of chord lengths of trajectory t, I t,α (Ω d ) : set of indexes of chord lengths of trajectory t that intersects region α, I t,α ∈ I t , r(i) : integer map such that r : i → α, giving for a chord i the region index α, r − t and r + t : incoming and outgoing points, respectively, of trajectory t.…”

Section: Linear Short Characteristics and Heterogeneous Cartesian Cel...mentioning

confidence: 99%

“…This geometrical mapping guarantees that the subdomains assigned to a process share at least one face, limiting, thus, the inter-node MPI communications. As an example of the subdomain splitting algorithm, Figure (6) illustrates an application on a 3x3x3 pivot grid distributed on 4 MPI processes.…”

Section: Automatic Construction Of the Pivot Grid The Cmfd Mesh And T...mentioning

confidence: 99%

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3D heterogeneous Cartesian cells for transport-based core simulations

Masiello

Lenain

Ford

2020

Annals of Nuclear Energy

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“…In conclusion we have brought to the solvers TDT and IDT (Masiello et al, 2009) of APOLLO3 R the λ and β quantities of the kinetic problem up to their fission iteration routines. And this not only for the kinetic problem itself, but also for the stationary one, since, as shown in Eq.…”

Section: Iterative Strategymentioning

confidence: 99%

A MOC-based neutron kinetics model for noise analysis

Gammicchia

Santandrea

Zmijarevic

et al. 2020

Annals of Nuclear Energy

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A 2-D noise model is implemented in the deterministic reactor code APOLLO3 R to simulate a periodic oscillation of a structural component. The Two/Three Dimensional Transport (TDT) solver, using the Method of Characteristics, is adopted for the calculation of the case studies, constituted by a moving detector and control-rod bundle. The periodic movement is built by properly linking the geometries corresponding to the temporal positions. The calculation is entirely performed in the real time domain, without resorting to the traditional frequency approach. A specifically defined dynamic eigenvalue is used to renormalize in average the reactivity over a period. The algorithm is accelerated by the DP N synthetic method. For each cell of the domain, the time values of fission rates are analysed to determine the noise extent. Moreover we propose a systematic approach to the definition of the macroscopic cross sections to be used in dynamical calculations starting from library data. As an aside of our work we have found that even in static calculation this approach can produce significant changes.

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New Numerical Solution with the Method of Short Characteristics for 2-D Heterogeneous Cartesian Cells in the APOLLO2 Code: Numerical Analysis and Tests

Cited by 19 publications

References 12 publications

Spherical Harmonics and Discontinuous Galerkin Finite Element Methods for the Three-Dimensional Neutron Transport Equation: Application to Core and Lattice Calculation

Spherical Harmonics and Discontinuous Galerkin Finite Element Methods for the Three-Dimensional Neutron Transport Equation: Application to Core and Lattice Calculation

3D heterogeneous Cartesian cells for transport-based core simulations

A MOC-based neutron kinetics model for noise analysis

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