Revealing the state space of turbulent pipe flow by symmetry reduction

Symmetry reduction by the method of slices is applied to pipe flow in order to quotient the stream-wise translation and azimuthal rotation symmetries of turbulent flow states. Within the symmetry-reduced state space, all travelling wave solutions reduce to equilibria, and all relative periodic orbits reduce to periodic orbits. Projections of these solutions and their unstable manifolds from their $\infty$-dimensional symmetry-reduced state space onto suitably chosen 2- or 3-dimensional subspaces reveal their interrelations and the role they play in organising turbulence in wall-bounded shear flows. Visualisations of the flow within the slice and its linearisation at equilibria enable us to trace out the unstable manifolds, determine close recurrences, identify connections between different travelling wave solutions, and find, for the first time for pipe flows, relative periodic orbits that are embedded within the chaotic attractor, which capture turbulent dynamics at transitional Reynolds numbers.Comment: 24 pages, 12 figure

Parametrising temperature dependent properties in thermal-mechanical analysis of power electronics modules using parametric Model Order Reduction

In this paper, a direct-coupled thermal-mechanical analysis of a Power Electronics Modules (PEM) using ANSYS-FEM (Finite Element Method) is integrated with a Parametric Model Order Reduction (pMOR) technique. Unlike most present studies on model order reduction, which perform the coupled thermal-mechanical analysis by sequential-coupled thermal-mechanical models, the direct-coupled thermal-mechanical approach deployed in this study solves the thermal and structural models simultaneously. Commonly, pMOR mainly focuses on parametrising model parameters (e.g., material properties, loads.) that are constants. In this investigation, a new approach to parametrise temperature-dependent properties using pMOR, such as the coefficient of thermal expansion (CTE) of the materials in PEM structures, has been demonstrated in the context of the reliability assessment of electronic modules. A two-dimensional finite element model of a PEM is developed and used to study the temperature-dependent CTE effects of the Aluminium (Al) alloy on the thermal-mechanical response of the system under thermal load. A Krylov subspace-based technique, PRIMA, has been used for the model order reduction and a linear approach of matrix interpolation for the parametrisation in the pMOR. The full-order state-space model has 30,612 degrees of freedom (DOFs), and the reduced model achieved by pMOR has just 8 DOFs. The simulation runs show that with this approach, a substantial reduction in computational time can be achieved, for this problem, by 81% between the full and the reduced order models. In modelling predictions, the pMOR-based solution has retained the accuracy of results. In this instance, the average difference in stress result, compared to the ANSYS-FEM model (FOM) solution, is only 0.43%

MODEL ORDER REDUCTION OF NONLINEAR DYNAMIC SYSTEMS USING MULTIPLE PROJECTION BASES AND OPTIMIZED STATE-SPACE SAMPLING

Model order reduction (MOR) is a very powerful technique that is used to deal with the increasing complexity of dynamic systems. It is a mature and well understood field of study that has been applied to large linear dynamic systems with great success. However, the continued scaling of integrated micro-systems, the use of new technologies, and aggressive mixed-signal design has forced designers to consider nonlinear effects for more accurate model representations. This has created the need for a methodology to generate compact models from nonlinear systems of high dimensionality, since only such a solution will give an accurate description for current and future complex systems.The goal of this research is to develop a methodology for the model order reduction of large multidimensional nonlinear systems. To address a broad range of nonlinear systems, which makes the task of generalizing a reduction technique difficult, we use the concept of transforming the nonlinear representation into a composite structure of well defined basic functions from multiple projection bases.We build upon the concept of a training phase from the trajectory piecewise-linear (TPWL) methodology as a practical strategy to reduce the state exploration required for a large nonlinear system. We improve upon this methodology in two important ways: First, with a new strategy for the use of multiple projection bases in the reduction process and their coalescence into a unified base that better captures the behavior of the overall system; and second, with a novel strategy for the optimization of the state locations chosen during training. This optimization technique is based on using the Hessian of the system as an error bound metric.Finally, in order to treat the overall linear/nonlinear reduction task, we introduce a hierarchical approach using a block projection base. These three strategies together offer us a new perspective to the problem of model order reduction of nonlinear systems and the tracking or preservation of physical parameters in the final compact model

Three-dimensional finite element analysis of earth pressure balance tunnelling

Ph.DDOCTOR OF PHILOSOPH

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science