Hybrid discrete (H TN) approximations to the equation of radiative transfer

The linear kinetic transport equations are ubiquitous in many application areas, including as a model for neutron transport in nuclear reactors and the propagation of electromagnetic radiation in astrophysics. The main computational challenge in solving the linear transport equations is that solutions live in a high-dimensional phase space that must be sufficiently resolved for accurate simulations. The three standard computational techniques for solving the linear transport equations are the (1) implicit Monte Carlo, (2) discrete ordinate(S$_N$), and (3) spherical harmonic(P$_N$) methods. Monte Carlo methods are stochastic methods for solving time-dependent nonlinear radiative transfer problems. In a traditional Monte Carlo method when photons are absorbed, they are reemitted in a distribution which is uniform over the entire spatial cell where the temperature is assumed constant, resulting in loss of information. In implicit Monte Carlo(IMC) methods, photons are reemitted from the place where they were actually absorbed, which improves the accuracy. Overall, IMC method improves stability, flexibility, and computational efficiency \cite{fleck}. The S$_N$ method solves the transport equation using a quadrature rule to reconstruct the energy density. This method suffers from so-called ray effect , which are due to the approximation of the double integral over a unit sphere by a finite number of discrete angular directions \cite{chai}. The P$_N$ approximation is based on expanding the part of the solution that depends on velocity direction (i.e., two angular variables) into spherical harmonics. A big challenge with the P$_N$ approach is that the spherical harmonics expansion does not prevent the formation of negative particle concentrations. The idea behind my research is to develop on an alternative formulation of P$_N$ approximations that hybridizes aspects of both P$_N$ and S$_N$. Although the basic scheme does not guarantee positivity of the solution, the new formulation allows for the introduction of local limiters that can be used to enforce positivity

Study of the Production of Isotopes in an Urban Nuclear Post-Detonation Environment

In order to model the activated isotopes and resulting dose from a nuclear detonation in an urban environment, the Activation and Transmutation of Isotopes in an Unstructured Mesh (ACTIUM) Python toolkit has been developed to combine the unstructured mesh- based particle transport capability of MCNP6 with the CINDER2008 transmutation code to produce quantities of interest for the post-detonation nuclear forensics and weapons effects communities. The ACTIUM toolkit has been implemented and validated with a number of test cases from a simple analytic model to a case study of the urban detonation in Nagasaki, Japan. The ACTIUM approach is the first of its kind to couple the latest release of CINDER2008 as a part of the Activation in Accelerator Radiation Environments (AARE) package with MCNP6 and produce transmuted quantities per time step on an unstructured mesh for the nuclear forensics and weapon effects communities. ACTIUM uses the latest ENDF/B-VIII.0, TENDL2017, and JENDL4 cross section libraries for the transmutation calculations, and includes methods for producing material cards for the initial MCNP6 unstructured mesh calculation based on highly detailed materials often found in urban environments on a city specific basis. In the event of an urban nuclear detonation, the identification of these isotopic ratios provides insight for the radio-analytical chemistry and mass-spectrometry communities as they develop measurement techniques to analyze some of the ratios that have the highest sensitivities to source attributes. A process of how to create an unstructured mesh representation of the overall geometry of buildings along with their material compositions, and the corresponding layers of concrete and soil in an urban environment for use in neutron transport calculations, and subsequent transmutation calculations are also discussed in this work

Coupling of Subchannel Analysis Tools with Advanced Multiscale Core Simulations

Nuclear reactors could allow to answer the energy demands and achieve low CO2 emissions in the country while nuclear simulation software can improve the efficiency without affecting the safety of nuclear reactors and therefore, the UK government is currently investing resources in the next generation of PWR and new nuclear simulation software. In nuclear reactors, the physical phenomena such as power production, heat and mass transfer, and fuel behaviour are coupled in between, although in nuclear simulation software, these physical phenomena have often been simulated independently. Several state-of-the-art multiscale and multi-physics software developments, including NURESIM and CASL, are being created, which include improved nuclear codes and coupling software environments. These cannot answer the demands of academia, the industry, and the nuclear regulator in the UK. NURESIM does not generally include the most advanced neutron transport methods, only providing improved coupled reactor physics. CASL generally requires thousands of processor/hours to deliver a solution which cannot be covered by the available computational clusters or workstations, providing full coupled reactor physics in all the reactor core. A multiscale and multi-physics software development is being created for the UK, which currently includes a nodal code, a transport code, a subchannel code, and a customized coupling software environment. It will eventually answer the demands of academia, the industry, and the nuclear regulator in the UK. It includes the most advanced neutron transport methods, providing simplified, improved, and full coupled reactor physics. It requires few processor/hours to deliver a solution which can be covered by the available computational clusters or workstations. It provides improved and full coupled reactor physics only in the hottest fuel assemblies with boundary conditions obtained providing simplified coupled reactor physics in all the reactor core. Validation and verification are fundamental for it to become state-of-the-art software. In this PhD project, the multiscale and multi-physics software development has been created along with its associated acknowledgements, validations, and verifications. These acknowledgements, validations, and verifications have outlined or proven several outcomes. Initially, an acknowledgement of the neutronics, thermal hydraulics, coupled reactor physics, SCALE-POLARIS code system lattice module, LOTUS, and Open MC transport codes, DYN3D nodal code, and CTF subchannel code were performed through their description. This has allowed an understanding of the theory used in the nuclear codes and of the nuclear codes used in later work. Then, validations and verifications of the accuracy and methodology available in CTF and FLOCAL (module of DYN3D) to provide thermal hydraulics at the fuel rod level were performed through the PSBT benchmark, previously covered by other partners using CTF, and through the FLOCAL developer benchmark not covered before. These have proven that CTF provides high accuracy in 1x1 and 5x5 bundles when compared to experimental data and other thermal hydraulics codes and a wide range of crossflow and turbulent mixing methods in a 2x1 bundle when compared to FLOCAL. Later, a one-way DYN3D and CTF coupling and the associated verification of the inner coupling iterations within an outer iteration were performed through the KAIST benchmark, previously tested by other partners using other neutronics codes, and through coupling scripts. These have proven that the DYN3D and CTF coupling provides improved feedback in 17x17 fuel assemblies compared to DYN3D using 1 processor within computational times of 20 minutes compared to 2 minutes. Then, a two-ways DYN3D and CTF coupling and the associated verification of the outer coupling iterations and convergence were performed through modified and created modules within DYN3D and a customized coupling software environment, and through the modified KAIST benchmark. These have proven that the DYN3D and CTF coupling provides improved coupled reactor physics in 17x17 fuel assemblies and 51x51 mini cores compared to DYN3D using 1 processor within computational times ranging from 1 to 10 hours compared to 2 to 20 minutes. Finally, a multi ways coupling between LOTUS, CTF and DYN3D and its associated verification were performed through the customized coupling software environment, and through the customized benchmark. These have proven that the LOTUS and CTF coupling with DYN3D provides full coupled reactor physics in a 3x3 quarter core with reflectors composed of 17x17 fuel assemblies or a 34x34 quarter core without reflectors compared to a DYN3D and CTF coupling with DYN3D applying parallelization across 36 processors within computational times ranging from 3 to 24 hours compared to 1 to 8 hours