Isogeometric finite element methods for liquid metal magnetohydrodynamics

A fusion blanket is a key component in a fusion reactor which extracts heat energy, protects the surrounding structure and possibly produces tritium, one of the fuels required for the deuterium-tritium fusion reaction. Interest in magneto-hydrodynamic (MHD) effects in the fusion blanket has been growing due to the promising prospect of a liquid breeder blanket, due to its high power density and the possibility of sustainable production of tritium. However, MHD effects can significantly influence the operating performance of the fusion blanket and an accurate and reliable analysis of the MHD effects are critical in its design. Significant progress in the numerical study of MHD has been made recently, due in large part to the advancement in computing power. However, its maturity has not yet reached a point comparable with standard CFD solvers. In particular, complex domains and complex externally applied magnetic fields present additional challenges for numerical schemes in MHD. For that reason, the application of isogeometric analysis is considered in this thesis. Isogeometric Analysis (IGA) is a new class of numerical method which integrates Computer Aided Design (CAD) into Finite Element Analysis (FEA). In IGA, B-splines and NURBS, which are the building blocks used to construct a geometry in CAD, are also used to build the finite element spaces. This allows to represent geometries more accurately, and in some cases exactly. This may help advance the progress of numerical studies of MHD effects, not only in fusion blanket scenarios, but more widely. In this thesis, we develop and study a number of types of IGA based MHD solver; a fully-developed MHD flow solver, a steady-state MHD solver and a time-dependent MHD solver. These solvers are validated using analytical methods and methods of manufactured solution and are compared with other numerical schemes on a number of benchmark problems.Open Acces