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In the high-temperature reactor design, it is common practice to leave gaps between the graphite blocks of the reflectors to accommodate thermal dilatation and material swelling, as well as to prov...

The Simplified P N ( S P N ) approximation is often used to model radiation transport phenomena, but it converges to the true solution of the transport equation only in one-dimensional slab geometr...

We introduce a (linear) positive and asymptotic-preserving method for solving the one-group radiation transport equation. The approximation in space is discretization agnostic: the space approximat...

In this paper, a group-wise Reduced-Order Model, based on a Proper Orthogonal Decomposition (POD) technique, is presented for parameterized multi-group diffusion k-eigenvalue problems. The group-wise approach is shown to be more robust than model-order reduction based on monolithic multi-group POD modes. In addition, fewer POD modes are required. The method of snapshots is employed to generate the offline training set. Two Naive and a Greedy snapshot-generation strategies are compared. The input parameter space is surveyed using Latin Hypercube Sampling techniques. The effectiveness of the group-wise model-order reduction method is demonstrated on two reactor-physics benchmarks, a two-group 3D Pressurized Water Reactor problem with 26 uncertain input parameters and a seven-group UO 2 -MOX fuel 3D mini-core with 287 uncertain input parameters. In both examples the Reduced-Order Models built using the snapshots generated by the Greedy algorithm proved to be slightly better. Model-order reduction yields results that are within 1 pcm of the full-order model, with speed-up factors of about 1000–3000, depending upon the test case.

The improved quasi-static method (IQS) is a rigorous space/time multiscale approach whereby the neutron flux is represented by a time-dependent amplitude and a time-, space-, and energy-dependent shape. The objective of the IQS factorization is to evaluate amplitude and shape on different time scales in order to reduce the computational burden associated with solving the multi-dimensional flux equations, while maintaining solution accuracy. The IQS decomposition leads to a nonlinear system of equations that requires iteration of shape and amplitude. IQS iteration techniques involve fixed-point (Picard) iteration with various convergence criteria and shape rescaling. Nonlinear convergence of each of these techniques is investigated. Verification of IQS with analysis of time step convergence is also investigated in order to examine the method’s effectiveness with high-order schemes. The time derivative of the shape function is discretized through fourth order using implicit-Euler, Crank-Nicolson, and backward difference formulae (BDF).

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

International audience; Modelling and simulation (M&S) have gradually become irreplaceable tools in the field of Nuclear Science and Technology (NS&T), including nuclear energy systems. This is partly due to growing computational resources and advances in computational science and partly to the difficulties to finance, build and license new experimental facilities. However, the utilization of M&S for research and development (R&D) and education and training (E&T) applications is somewhat hampered by limited accessibility to controlled and sensitive nuclear M&S tools as well as by the desires of the developers of these tools to retain their intellectual property (IP). Open-source software and open-access data are growingly perceived as means to accelerate innovation by promoting synergistic collaborative developments while lowering the barriers associated to code distribution, modification, and sharing. Open-source software development is ideal for R&D and E&T purposes because it permits the enhancement of understanding, the use of advanced computational methods and it promotes the cooperation among researchers and scientists, without rigorous constraints on quality assurance or reliance on proprietary data for technology-specific validation. As a fundamental research tool, this helps to mitigate constraints related to dual use of such technology. It is in this context that an initiative is being launched under the aegis of the International Atomic Energy Agency (IAEA) to promote the development and application of open-source multi-physics simulation in support of R&D and E&T in NS&T. This paper presents scope and objectives of this initiative.

Discontinuous Finite Element Methods (DFEM) have been widely used for solving SN radiation transport problems in participative and non-participative media. In this method, small matrix-vector systems are assembled and solved for each cell, angle, energy group, and time step while sweeping through the computational mesh. In practice, these systems are generally solved directly using Gaussian elimination, as computational acceleration for solving this small systems are often inadequate. Nonetheless, the computational cost of assembling and solving these local systems, repeated for each cell in the phase-space, can amount to a large fraction of the total computing time. In this paper, a Machine Learning algorithm is designed to accelerate the solution of local systems. This one is based on Artificial Neural Networks (ANNs). Its key idea is training an ANN with a large set of solutions to random one-cell transport problems and, then, replacing the assembling and solution of the local systems by the feedforward evaluation of the trained ANN. It is observed that the optimized ANNs are able to reduce the compute times by a factor of ~ 3:6 per source iteration, while introducing mean absolute errors between 0:5 – 2% in transport solutions.

This paper uses local dual weighted residual (DWR) error indicators to flag cells for goal-based refinement in a 1-D diamond difference (DD) discretisation of the discrete ordinate (SN) neutron transport equations. Goal-orientated adaptive mesh refinement (GO-AMR) aims to produce a mesh that is optimal for a given goal or QoI (Quantity of Interest). h, p and hp refinement is implemented and applied to various test cases. A merit function is derived for the combined hp algorithm and is calculated for each refinement option within each flagged cell. The refinement option with the highest merit function is chosen for a given flagged cell. This paper also investigates the use of the DWR error estimation as a correction term for the originally calculated QoI. If error correction and GO-AMR are combined the DWR error indicators do not always give an optimal mesh for the corrected value of the QoI. Therefore, refinement indicators based on the error in the error correction term are used and tested in this work.

This work presents an assessment of the capabilities of RELAP-7, the next-generation nuclear reactor system code, to solve single- and two-phase flows developing shock tubes and gravity waves. RELAP-7 is based on a seven-equation two-phase flow model with distinct phasic pressures. It is well established that these hyperbolic conservation laws can develop shocks and discontinuities thus requiring a stabilization numerical method. The all-Mach flow Entropy Viscosity Method (EVM) is now employed in RELAP-7 as a viscous stabilization approach. This paper briefly describes implementation of the EVM and uses open-literature test cases that exhibit pressure and gravity waves to show that the entropy viscosity method performs adequately for these single- and two-phase cases.

This article focuses on parametric reduced-order models to decrease the computational cost of large-scale neutron transport problems in the atmosphere. The atmospheric humidity content and neutron source spectrum are considered as uncertain parameters throughout the problem. We first present our full-order model, including an axisymmetric S N transport methodology, a geopotential model for computing the thermophysical properties of the atmosphere, and a support vector regression method for rapidly generating one-group cross sections at every point. Then, reduction of the full-order problem using the POD-Galerkin and least-squares POD-Petrov-Galerkin methods is presented. The reduced-order models implemented introduce mean relative errors between 0.06% and 0.4% with acceleration factors between 3.6 × 10 3 - 8.4 × 10 4 , respectively.

This paper compares pressure reconstruction strategies in Model Order Reduction for incompressible flows with convective heat transfer. The Navier-Stokes equation are reduced along with the passive scalar transport equation for the temperature using the POD-Galerkin technique. Six different pressure reconstruction methods are evaluated, two of which are novel to the best of the authors’ knowledge. Accurate pressure reconstruction is key to avoid error buildup in when solving for the conservation of linear momentum at the reduced level. The six approaches are compared using Direct Numerical Simulations of convective heat exchange processes in a 3D Backward Facing Step with a heated cylinder. When comparing time-averaged metrics, we observe that the reconstruction methods that approximate the reduced pressure field using techniques borrowed from full order models (mechanical analogy, pressure Poisson, and velocity supremizers) yield higher errors than the methods that seek to stabilize the reduced systems (reduced residual stabilization, artificial divergence, and Uzawa operator).

Summary In [1], a viscous regularization technique, based on the local entropy residual, was proposed to stabilize the nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, the work in [1] was only based on the hyperbolic parts of the Grey Radiation-Hydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here, we extend the theoretical grounds for the method and derive an entropy minimum principle for the full set of nonequilibrium-diffusion Grey Radiation Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiation-hydrodynamic shock simulations. Radiative shock calculations using constant and temperature-dependent opacities are compared against semi-analytical reference solutions and we present a procedure to perform spatial convergence studies of such simulations. This article is protected by copyright. All rights reserved.

Historically, matrix lumping and ad hoc flux fixups have been the only methods used to eliminate or suppress negative angular flux solutions associated with the unlumped bilinear discontinuous (UBL...

In Allmaras et al. [Inverse Prob. Imaging, Vol. 7, No. 1, p. 47 (2013)], we present the mathematical foundations for the passive detection of small low-emission radioactive sources buried in backgr...