Multiscale, multiphysics and reduced order modelling techniques for hemodynamics.

Usage of numerical modelling techniques in a clinical setting is limited due to the computational resources and modelling expertise required. This thesis focuses on multiscale modelling and model order reduction as tools to reduce the computational cost and improving model robustness of hemodynamical models. Firstly, it is shown, using data for an aortic flow phantom, that integration of patient-specific data favours a multiscale approach due to measurement uncertainties leading to a violation of the conservation of mass and momentum. Stability of different multiscale model coupling schemes for partitioned modelling is addressed, demonstrating the superior stability of central-difference based schemes compared to more traditional explicit and semi-implicit schemes. This is highly relevant for the application of large artery modelling due to the potentially large number of models coupled simultaneously, including boundary condition models and Fluid-structure interaction (FSI). A compressible fluid model capable of representing 3D wave propagation at reduced cost is analysed in order to suggest improvements for increased accuracy. Additionally, this part considers the limitations and functional difference between a 1D wave propagation, compressible fluid and 2-way FSI model. Lastly, a proof of concept is given for reduced order models (ROMs) of 3D field data in medicine using a singular value decomposition based approach. Effects of the choice and normalisation of training data on the SVD basis and ROM are explored. This ultimately leads to generation of a 3D transient ROM of the pressure field within a sudden expansion at an average percentual error of 0.45[%].