An angular reduced order model for radiative transfer in non grey media

This paper investigates a reduced order model for the angular discretisation of the radiative transfer equation (RTE) when considering non grey participating gases. The key idea is to use a global model for the gas radiative properties and to derive an angular reduced order model, based on the Proper Orthogonal Decomposition (POD) method, for each absorption coefficient class independently. Angular POD basis functions are extracted from high order SN reference solutions. A finite element approach is used to discretised the RTE in space and angle and the POD angular matrices of the reduced system are easily constructed from the SN angular matrices of the reference solutions. The angular POD basis sets are truncated at different levels depending on the absorption coefficient class in order to optimally compute the total radiative power. The method is applied to solve the radiation field associated to an air/H2O mixture flowing in a square differentially heated cavity, with black isothermal walls and diffuse reflecting adiabatic walls. Results show that the POD model is very accurate and efficient for treating the thick classes but it suffers from a low convergence rate for the thin classes. For computing the radiative power, the reduced order model allows to reduce the averaged number of angular basis functions of an order of magnitude and to reduce the CPU time by a factor 2 to 3 to reach a given level of accuracy, compared to a standard SN method

Reduced-Order Modelling Applied to the Multigroup Neutron Diffusion Equation Using a Nonlinear Interpolation Method for Control-Rod Movement

Producing high-fidelity real-time simulations of neutron diffusion in a reactor is computationally extremely challenging, due, in part, to multiscale behaviour in energy and space. In many scientific fields, including nuclear modelling, the application of reduced-order modelling can lead to much faster computation times without much loss of accuracy, paving the way for real-time simulation as well as multi-query problems such as uncertainty quantification and data assimilation. This paper compares two reduced-order models that are applied to model the movement of control rods in a fuel assembly for a given temperature profile. The first is a standard approach using proper orthogonal decomposition (POD) to generate global basis functions, and the second, a new method, uses POD but produces global basis functions that are local in the parameter space (associated with the control-rod height). To approximate the eigenvalue problem in reduced space, a novel, nonlinear interpolation is proposed for modelling dependence on the control-rod height. This is seen to improve the accuracy in the predictions of both methods for unseen parameter values by two orders of magnitude for keff and by one order of magnitude for the scalar flux

Solving the discretised neutron diffusion equations using neural networks

This paper presents a new approach which uses the tools within artificial intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical methods. In particular, we describe how to represent numerical discretisations arising from the finite volume and finite element methods by pre-determining the weights of convolutional layers within a neural network. As the weights are defined by the discretisation scheme, no training of the network is required and the solutions obtained are identical (accounting for solver tolerances) to those obtained with standard codes often written in Fortran or C++. We also explain how to implement the Jacobi method and a multigrid solver using the functions available in AI libraries. For the latter, we use a U-Net architecture which is able to represent a sawtooth multigrid method. A benefit of using AI libraries in this way is that one can exploit their built-in technologies to enable the same code to run on different computer architectures (such as central processing units, graphics processing units or new-generation AI processors) without any modification. In this article, we apply the proposed approach to eigenvalue problems in reactor physics where neutron transport is described by diffusion theory. For a fuel assembly benchmark, we demonstrate that the solution obtained from our new approach is the same (accounting for solver tolerances) as that obtained from the same discretisation coded in a standard way using Fortran. We then proceed to solve a reactor core benchmark using the new approach. For both benchmarks we give timings for the neural network implementation run on a CPU and a GPU, and a serial Fortran code run on a CPU

Improved estimates of 222 nm far-UVC susceptibility for aerosolized human coronavirus via a validated high-fidelity coupled radiation-CFD code.

Transmission of SARS-CoV-2 by aerosols has played a significant role in the rapid spread of COVID-19 across the globe. Indoor environments with inadequate ventilation pose a serious infection risk. Whilst vaccines suppress transmission, they are not 100% effective and the risk from variants and new viruses always remains. Consequently, many efforts have focused on ways to disinfect air. One such method involves use of minimally hazardous 222 nm far-UVC light. Whilst a small number of controlled experimental studies have been conducted, determining the efficacy of this approach is difficult because chamber or room geometry, and the air flow within them, influences both far-UVC illumination and aerosol dwell times. Fortunately, computational multiphysics modelling allows the inadequacy of dose-averaged assessment of viral inactivation to be overcome in these complex situations. This article presents the first validation of the WYVERN radiation-CFD code for far-UVC air-disinfection against survival fraction measurements, and the first measurement-informed modelling approach to estimating far-UVC susceptibility of viruses in air. As well as demonstrating the reliability of the code, at circa 70% higher, our findings indicate that aerosolized human coronaviruses are significantly more susceptible to far-UVC than previously thought

Angular adaptivity with spherical harmonics for Boltzmann transport

This paper describes an angular adaptivity algorithm for Boltzmann transport applications which uses Pn and filtered Pn expansions, allowing for different expansion orders across space/energy. Our spatial discretisation is specifically designed to use less memory than competing DG schemes and also gives us direct access to the amount of stabilisation applied at each node. For filtered Pn expansions, we then use our adaptive process in combination with this net amount of stabilisation to compute a spatially dependent filter strength that does not depend on a priori spatial information. This applies heavy filtering only where discontinuities are present, allowing the filtered Pn expansion to retain high-order convergence where possible. Regular and goal-based error metrics are shown and both the adapted Pn and adapted filtered Pn methods show significant reductions in DOFs and runtime. The adapted filtered Pn with our spatially dependent filter shows close to fixed iteration counts and up to high-order is even competitive with P0 discretisations in problems with heavy advection.Comment: arXiv admin note: text overlap with arXiv:1901.0492

Scalable angular adaptivity for Boltzmann transport

This paper describes an angular adaptivity algorithm for Boltzmann transport applications which for the first time shows evidence of $\mathcal{O}(n)$ scaling in both runtime and memory usage, where $n$ is the number of adapted angles. This adaptivity uses Haar wavelets, which perform structured $h$-adaptivity built on top of a hierarchical P$_0$ FEM discretisation of a 2D angular domain, allowing different anisotropic angular resolution to be applied across space/energy. Fixed angular refinement, along with regular and goal-based error metrics are shown in three example problems taken from neutronics/radiative transfer applications. We use a spatial discretisation designed to use less memory than competing alternatives in general applications and gives us the flexibility to use a matrix-free multgrid method as our iterative method. This relies on scalable matrix-vector products using Fast Wavelet Transforms and allows the use of traditional sweep algorithms if desired