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

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.