Adaptive hierarchical radiation transport methods to meet future challenges in reactor physics

这一提议提出之际，英国核部门正在复苏。现在人们普遍认为，英国履行其减少二氧化碳排放的承诺以及应对过度依赖进口燃料供应的方法之一是更换目前老化的核反应堆。然而，近年来，英国训练有素的科学家和工程师大幅减少，这种技能短缺现在正接近临界点。除非立即采取行动，否则熟练的劳动力将太少，无法监督现有核电设施的安全运行、退役和废物处理，更不用说满足未来任何新建设的需求了。此外，从新反应堆设计到废物处理，许多与核有关的问题仍然没有解决，因此，增加我们的专业知识以及我们对核的理解是非常重要的。在本提案中，我们将通过开发新的辐射输运建模（RT）方法来解决许多主要问题。这将加强我们对反应堆物理、辐射屏蔽和辐射损害、临界安全和废物处理等一系列领域的了解。这将使英国重新站在RT研究的前沿。它还将为参与能源和环境倡议的政策制定者、科学家和工程师提供信息，并增强对核安全和废物处理的信心。这部分是由于描述辐射传输的7维相空间的高度复杂性，而且反应堆堆芯内固有的多尺度几何形状超出了大多数数值方案的建模能力。因此，多尺度、降阶和自适应数值方法对反应堆物理的这一领域是非常有价值的。它们可以将从最小的燃料元件到最大的燃料阵列的众多长度尺度连接在一起，具有数学严谨性，同时形成计算效率高且快速的解决方案。拟议的工作将通过首次开发实现这一潜力：1）用于RT的完整多尺度模型，其严格地链接用于反应堆物理应用的所有长度尺度。2）嵌入式降阶方法，其通过将大尺度模型减少到仅几百个未知量而将计算复杂性显著地降低了几个数量级。3）误差估计，其实现了能够解析完整7 D相空间的自适应能力，并将计算资源集中于解析关键物理，因此可以在不影响准确性的情况下提高效率。4）并行求解器技术，用于有效解决大规模问题，可在当前和未来的多核计算机平台上执行。嵌入式数据同化方法，将上述技术与已知的核数据不确定性联系起来，以形成解和其他关键参数的误差范围。这将提供关于不确定性的新信息，由于几何形状、材料数据和其他输入参数的变化而导致的灵敏度和误差。我们这个项目的总体目标是使用世界领先的模型准确预测RT。新技术包括;多尺度方法、降阶模型、误差估计、自适应性、数据同化和并行求解器将在我们的有限元RT模型框架RADIONT中实施。通过提供一个具有先进数值技术的模型，准确地捕捉复杂的几何细节，结合对误差和敏感性的估计，我们可以使用户能够对广泛的核应用做出明智的判断。这将产生广泛的影响，例如，向政府和监管机构提供信息，提高公司和利益攸关方的能力，并确保科学界的研究方法是最先进的。这将有助于增加信心、减少错误和降低风险。

This proposal comes at a time when the UK nuclear sector is resurgent. It is now widely accepted that one of the ways in which the UK can meet its commitments to reducing CO2 emissions, as well as dealing with its over-reliance on imported fuel supplies, is to replace the current fleet of ageing nuclear reactors. However, in recent years the UK has seen a substantial reduction in trained scientists and engineers and this skills shortage is now approaching a critical point. Unless immediate action is taken the skilled work force will be too small to oversee safe operation, decommissioning and waste disposal from the current nuclear power facilities, let alone satisfy demand driven by any future new build. In addition, many nuclear related issues also remain unsolved, from new reactor designs to waste disposal, and so increasing our expertise as well as our understanding in nuclear is of great importance. In this proposal we will address many of the main issues by developing novel approaches for radiation transport modelling (RT). This will enhance our understanding across a range of fields from reactor physics, radiation shielding and radiation damage to criticality safety and waste disposal. This will put the UK back at the forefront of RT research. It will also inform policy makers, scientists and engineers involved in energy and environmental initiatives and increase confidence in nuclear safety and waste disposal.RT modelling has been notoriously difficult. This is partly due to the high complexity of the 7 dimensional phase-space that describes radiation transport, but also the inherent multi-scale geometries within reactor cores are beyond the modelling capabilities of most numerical schemes. Multi-scale, reduced order, and adaptive numerical methods can therefore be extremely valuable to this area of reactor physics. They can link together the numerous length-scales, from the smallest fuel element to the largest fuel arrays, with mathematical rigour whilst forming computationally efficient and fast solutions. The proposed work will realise this potential by developing, for the first time:1) A full multi-scale model for RT that rigorously links all length scales for reactor physics applications.2) Embedded reduced order methods that significantly reduce computational complexity by several orders of magnitude through the reduction of large scale models to only a few hundred unknowns.3) Error estimates that enable adaptive capabilities which can resolve the full 7D phase-space & focus computing resources on resolving the key physics, therefore increasing efficiency without compromising accuracy.4) Parallel solver technologies for the efficient solution of large scale problems that can be carried out on current & future multi-core computer platforms.5) Embedded data assimilation methods that link the above technologies with known nuclear data uncertainties to form error bounds on solutions & other key parameters.This will provide new information on uncertainties, sensitivities & errors resulting from variations in geometry, material data and other input parameters.Our overall aim of this project is the accurate prediction of RT using a world leading model. The novel technologies including; multi-scale methods, reduced order models, error estimates, adaptivity, data assimilation and parallel solvers will be implemented within our finite element RT model framework RADIANT. By providing a model with advanced numerical technologies that accurately capture intricate geometric detail, combined with estimates of errors and sensitivities, we can enable the user to make informed judgements on a wide range of nuclear applications. This will have wide ranging impacts, e.g. informing government and regulatory bodies, enhancing company and stakeholder capabilities and ensuring that the scientific communities research methodologies are cutting edge. This will serve to increase confidence, mitigate errors and reduce risk.