Discontinuous and Continuous Virtual Element Methods (VEM) for Robust Meshing and Modelling of Complex Geometries in Radiation Shielding Analysis and

项目摘要：这一特定的PHD项目涉及开发多边形和多面体非结构网格虚拟单元方法，用于提供稳态中子扩散和中子迁移方程的几何一致性空间离散。这些方法将提供数值稳健的离散化，能够在高度扭曲的网格上求解偏微分方程组。此外，与传统的基于有限元的空间离散方法相比，这些方法具有很高的精度和计算效率。这些新的数值格式的应用将在核反应堆物理和辐射屏蔽领域，特别是对用于海军推进和发电的小型模块反应堆(SMR)进行建模。

Project Summary: This particular PhD projects involves the development of polygonal and polyhedral unstructured mesh virtual element methods for providing geometry conforming spatial discretisations of the steady-state neutron diffusion and neutron transport equation. These method will provide numerical robust discretisation which are able to solve partial differential equations on highly-distorted meshes. In addition these methods are very high-order accurate and more computationally efficient than conventional finite element based spatial discretisations. The application of these novel numerical schemes will be in the field of nuclear reactor physics and radiation shielding with particular relevance to modelling small modular reactors (SMRs) for naval propulsion and power generation.