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Reactor design requires safety studies to ensure that the reactors will behave appropriately under incidental or accidental situations. Safety studies often involve multiphysics simulations where several branches of reactor physics are necessary to model a given phenomenon. In those situations, it has been observed that the neutron transport part is still a bottleneck in terms of computational times, with more than 80% of the total time. In the case of hexagonal lattice reactors, transport solvers usually invert the discretised Boltzmann equation by discretising the regular hexagon into lozenges or triangles. In this work, we seek to reduce the computational burden of the neutron transport solver by designing a numerical spatial discretisation scheme that would be more appropriate for honeycomb meshes. In our past research efforts, we have set up interesting discretisation schemes in the finite element setting in 2D, and we wish to extend them to 3D geometries that are prisms with a hexagonal base. In 3D, a rigorous method was derived to shrink the tensor product between 2D and 1D bases to minimum terms. We have applied these functions successfully on a reactor benchmark—Takeda Model 4—to compare and contrast the numerical results in a physical setting. [ABSTRACT FROM AUTHOR]

This work focuses on the k-eigenvalue problem of the neutron transport equation. The variables of interest are the largest eigenvalue (keff) and the corresponding eigenmode is called the fundamental mode. Mathematically, this problem is usually solved using the power iteration method. However, the convergence of this algorithm can be very slow, especially if the dominance ratio is high as is the case in some reactor physics applications. Thus, the power iteration method has to be accelerated in some ways to improve its convergence. One such acceleration is the Chebyshev acceleration method which has been widely applied to legacy codes. In recent years, nonlinear methods have been applied to solve the k-eigenvalue problem. Nevertheless, they are often compared to the unaccelerated power iteration. Hence, the goal of this paper is to apply the Anderson acceleration to the power iteration, and compare its performance to the Chebyshev acceleration.

Presently, APOLLO3® /MINARET solves the transport equation using the multigroup Sn method with discontinuous finite elements on triangular meshes with Lagrange polynomial bases. The goal of this work is to solve the spatial problem on hexagonal geometries in the context of honeycomb lattice reactors, without further refining the computational mesh. The idea here is to construct high-order basis functions on the hexagonal element in order to improve the trade-off between computational cost and accuracy, in particular for multiphysics simulations where, often, thermalhydraulic modelling requires only assembly-average cross-sections to be defined (e.g. severe accident of fast breeder reactors) i.e. the assemblies are assumed homogeneous. One approach to achieve this goal is through the use of generalised barycentric functions such as the Wachspress rational functions. This research endeavour deals with the application of Wachspress rational functions to the neutron transport equation for hexagonal geometries up to order 3. With this method, it is possible to decrease the number of spatial unknowns required for the same accuracy, and thus the computational burden for complex geometries, such as honeycomb lattices is reduced.

In the context of the simulation of the Severe Accidents (SA) in Light Water Reactors (LWR), we are interested on the in-core corium pool propagation transient in order to evaluate the corium relocation in the vessel lower head. The goal is to characterize the corium and debris flows from the core to accurately evaluate the corium pool propagation transient in the lower head and so the associated risk of vessel failure. In the case of LWR with heavy reflector, to evaluate the corium relocation into the lower head, we have to study the risk associated with focusing effect and the possibility to stabilize laterally the corium in core with a flooded down-comer. It is necessary to characterize the core degradation and the stratification of the corium pool that is formed in core. We assume that the core degradation until the corium pool formation and the corium pool propagation could be modeled separately. In this document, we present a simplified geometrical model (0D model) for the in-core corium propagation transient. A degraded core with a formed corium pool is used as an initial state. This state can be obtained from a simulation computed with an integral code. This model does not use a grid for the core as integral codes do. Geometrical shapes and 0D models are associated with the corium pool and the other components of the degraded core (debris, heavy reflector, core plate…). During the transient, these shapes evolve taking into account the thermal and stratification behavior of the corium pool and the melting of the core surrounding components. Some results corresponding to the corium pool propagation in core transients obtained with this model on a LWR with a heavy reflector are given and compared to grid approach of the integral codes MAAP4.

Considering transient processes where liquid/solid phase change occurs, this paper focuses on the associated modeling and numerical treatment in the frame of "Computational Fluid Dynamics" simulations. While being of importance in many industrial applications involving solidification and melting of mixed materials, including power and manufacturing engineering, the first application of this work pertains to the analysis of severe accidents in a nuclear reactor. Indeed, in this context, the molten core materials (a.k.a. corium) can form a high-temperature multiphase liquid pool at the boundary of which fusion and solidification phenomena are of prime importance. In this context, even if materials at play are treated as pure components, it is mandatory to distinguish two different phase change temperatures with a solid fusion temperature and a liquid solidification temperature. Accordingly, in the frame of a sharp interface representation, the paper introduces non-classical heterogeneous conditions at the liquid/solid boundary in such a way that both moving interface (through Stefan conditions associated with fusion or solidification) and static interface (imposing heat flux continuity) are supported at the same time on different spatial locations along this boundary. Within a monolithic resolution of Navier–Stokes and heat conduction equations, this interface is explicitly tracked with combined Front-Tracking and VOF methods. In order to ensure zero velocity in the solid phase, an Immersed Boundary Method and a direct forcing penalization are also introduced. The main relevant features of this combination of numerical methods are discussed along with their implementation in the TrioCFD code taking advantage of the pre-existing code capabilities. Numerical simulations including both verification tests and a case of interest for our industrial application are reported and demonstrate the applicability of the proposed triptych model+methods+code to treat such problems. The numerical tools and the simulation code developed in this work could be used not only in the several accident context but also to simulate melting, solidification and fusion processes occurring in aerodynamics, hypersonic reentry vehicles and laser applications to cite but a few. [ABSTRACT FROM AUTHOR]

AbstractThis paper describes the implementation of efficient and portable vectorized sweep kernels as part of the resolution of the neutron transport equation on three-dimensional Cartesian grids using the discrete ordinates ($${{\mathcal S}_n}$$Sn) method for the angular variable and the diamond differencing (DD) scheme for the spatial discretization. Vectorization is set up along the directions within the same octant and is independent of the spatial discretization order; therefore, the extension of this technique to high-order DD or discontinuous Galerkin schemes is immediate. Our implementation is written in C++17 and relies on the Kokkos performance portability framework. This library allows one to express shared-memory parallelism (including vectorization) in a machine-independent way and supports many backends including CUDA and OpenMP. Our vectorization procedure relies on the portable single instruction multiple data types provided by Kokkos. The method has been implemented for DD schemes up to order 2 and yields promising results on CPUs supporting standard vector instructions. [ABSTRACT FROM AUTHOR]