Abstract

Latest developments in high-strength Magnetic Resonance Imaging (MRI) scanners with in-built high resolution, have dramatically enhanced the ability of clinicians to diagnose tumours and rare illnesses. However, their high-strength transient magnetic fields induce unwanted eddy currents in shielding components, which result in fast vibrations, noise, imaging artefacts and, ultimately, heat dissipation, boiling off the helium used to super-cool the magnets. Optimum MRI scanner design requires the capturing of complex electro-magneto-mechanical interactions with high fidelity computational tools. During production cycles, this is known to be extremely expensive due to the large number of configurations that need to be tested. There is an urgent need for the development of new cost-effective methods whereby previously performed computations can be assimilated as training solutions of a surrogate digital twin model to allow for real-time simulations. In this paper, a Reduced Order Modelling technique based on the Proper Generalised Decomposition method is presented for the first time in the context of MRI scanning design, with two distinct novelties. First, the paper derives from scratch the offline higher dimensional parametrised solution process of the coupled electro-magneto-mechanical problem at hand and, second, a regularised adaptive methodology is proposed for the circumvention of numerical singularities associated with the ill-conditioning of the discrete system in the vicinity of resonant modes. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and flexibility of the considered approach.

Abstract

The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different geometrical parameter values and also allowing to compute readily the sensitivities. Instead of problem dependent approaches, a general framework is presented for standard engineering environments where the geometry is defined by means of NURBS. The parameters controlling the geometry are now the control points characterising the NURBS curves or surfaces. The approach proposed here, valid for 2D and 3D scenarios, allows a seamless integration with CAD preprocessors. The proper generalised decomposition (PGD), which is applied here to compute explicit geometrically parametrised solutions, circumvents the curse of dimensionality. Moreover, optimal convergence rates are shown for PGD approximations of incompressible flows

Abstract

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper generalised decomposition (PGD) in OpenFOAM, for the approximation of parametrised laminar incompressible Navier–Stokes equations. The key feature of this approach is the seamless integration of a reduced order model (ROM) in the framework of an industrially validated computational fluid dynamics software. This is of special importance in an industrial environment because in the online phase of the PGD ROM the description of the flow for a specific set of parameters is obtained simply via interpolation of the generalised solution, without the need of any extra solution step. On the one hand, the spatial problems arising from the PGD separation of the unknowns are treated using the classical solution strategies of OpenFOAM, namely the semi-implicit method for pressure linked equations (SIMPLE) algorithm. On the other hand, the parametric iteration is solved via a collocation approach. The resulting ROM is applied to several benchmark tests of laminar incompressible Navier–Stokes flows, in two and three dimensions, with different parameters affecting the flow features. Eventually, the capability of the proposed strategy to treat industrial problems is verified by applying the methodology to a parametrised flow control in a realistic geometry of interest for the automotive industry.