Adaptive mesh refinement for computational aeroacoustics

UNIVERSITY OF SOUTHAMPTON ABSTRACT FACULTY OF ENGINEERING, SCIENCE & MATHEMATICS SCHOOL OF ENGINEERING SCIENCES Doctor of Philosophy ADAPTIVE MESH REFINEMENT FOR COMPUTATIONAL AEROACOUSTICS by Xun HuangThis thesis describes a parallel block-structured adaptive mesh refinement (AMR) method that is employed to solve some computational aeroacoustic problems with the aim of improving the computational efficiency. AMR adaptively refines and coarsens a computational mesh along with sound propagation to increase grid resolution only in the area of interest. While sharing many of the same features, there is a marked difference between the current and the established AMR approaches. Rather than low-order schemes generally used in the previous approaches, a high-order spatial difference scheme is employed to improve numerical dispersion and dissipation qualities. To use a high-order scheme with AMR, a number of numerical issues associated with fine-coarse block interfaces on an adaptively refined mesh, such as interpolations, filter and artificial selective damping techniques and accuracy are addressed. In addition, the asymptotic stability and the transient behaviour of a high-order spatial scheme on an adaptively refined mesh are also studied with eigenvalue analysis and pseudospectra analysis respectively. In addition, the fundamental AMR algorithm is simplified in order to make the work of implementation more manageable. Particular emphasis has been placed on solving sound radiation from generic aero-engine bypass geometry with mean flow. The approach of AMR is extended to support a body-fitted multi-block mesh. The radiation from an intake duct is modelled by the linearised Euler equations, while the radiation from an exhaust duct is modelled by the extended acoustic perturbation equations to suppress hydrodynamic instabilities generated in a sheared mean flow. After solving the near-field sound solution, the associated far-field sound directivity is estimated by solving the Ffowcs Williams-Hawkings equation. The overall results demonstrate the accuracy and the efficiency of the presented AMR method, but also reveal some limitations. The possible methods to avoid these limitations are given at the end of this thesis

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Modelling for robust feedback control of fluid flows

This paper addresses the problem of designing low-order and linear robust feedback controllers that provide a priori guarantees with respect to stability and performance when applied to a fluid flow. This is challenging, since whilst many flows are governed by a set of nonlinear, partial differential–algebraic equations (the Navier–Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are: firstly, linear; secondly, described by ordinary differential equations (ODEs); and thirdly, finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the H∞ loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl’s theory of sheared turbulence. To illustrate the application of these techniques, an H∞ loop-shaping controller is designed and applied to the problem of reducing perturbation wall shear stress in plane channel flow. Direct numerical simulation (DNS) results demonstrate robust attenuation of the perturbation shear stresses across a wide range of Reynolds numbers with a single linear controller

Modelling for Robust Feedback Control of Fluid Flows

This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial differential-algebraic equations (the Navier-Stokes equations), the majority of established control theory assumes models of much greater simplicity, in that they are firstly: linear, secondly: described by ordinary differential equations, and thirdly: finite-dimensional. Linearisation, where appropriate, overcomes the first disparity, but attempts to reconcile the remaining two have proved difficult. This paper addresses these two problems as follows. Firstly, a numerical approach is used to project the governing equations onto a divergence-free basis, thus converting a system of differential-algebraic equations into one of ordinary differential equations. This dispenses with the need for analytical velocity-vorticity transformations, and thus simplifies the modelling of boundary sensing and actuation. Secondly, this paper presents a novel and straightforward approach for obtaining suitable low-order models of fluid flows, from which robust feedback controllers can be synthesised that provide~\emph{a~priori} guarantees of robust performance when connected to the (infinite-dimensional) linearised flow system. This approach overcomes many of the problems inherent in approaches that rely upon model-reduction. To illustrate these methods, a perturbation shear stress controller is designed and applied to plane channel flow, assuming arrays of wall mounted shear-stress sensors and transpiration actuators. DNS results demonstrate robust attenuation of the perturbation shear-stresses across a wide range of Reynolds numbers with a single, linear controller

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Despite the important role that WiFi networks play in home and enterprise networks they are relatively weak from a security standpoint. With easily available directional antennas, attackers can be physically located off-site, yet compromise WiFi security protocols such as WEP, WPA, and even to some extent WPA2 through a range of exploits specific to those protocols, or simply by running dictionary and human-factors attacks on users' poorly-chosen passwords. This presents a security risk to the entire home or enterprise network. To mitigate this ongoing problem, we propose SecureArray, a system designed to operate alongside existing wireless security protocols, adding defense in depth against active attacks. SecureArray's novel signal processing techniques leverage multi-antenna access point (AP) to profile the directions at which a client's signals arrive, using this angle-of-arrival (AoA) information to construct highly sensitive signatures that with very high probability uniquely identify each client. Upon overhearing a suspicious transmission, the client and AP initiate an AoA signature-based challenge-response protocol to confirm and mitigate the threat. We also discuss how SecureArray can mitigate direct denial-of-service attacks on the latest 802.11 wireless security protocol. We have implemented SecureArray with an eight-antenna WARP hardware radio acting as the AP. Our experimental results show that in a busy office environment, SecureArray is orders of magnitude more accurate than current techniques, mitigating 100% of WiFi spoofing attack attempts while at the same time triggering false alarms on just 0.6% of legitimate traffic. Detection rate remains high when the attacker is located only five centimeters away from the legitimate client, for AP with fewer numbers of antennas and when client is mobile

An Efficient, Memory-Saving Approach for the Loewner Framework

The Loewner framework is one of the most successful data-driven model order reduction techniques. If N is the cardinality of a given data set, the so-called Loewner and shifted Loewner matrices [Formula: see text] and [Formula: see text] can be defined by solely relying on information encoded in the considered data set and they play a crucial role in the computation of the sought rational model approximation.In particular, the singular value decomposition of a linear combination of [Formula: see text] and [Formula: see text] provides the tools needed to construct accurate models which fulfill important approximation properties with respect to the original data set. However, for highly-sampled data sets, the dense nature of [Formula: see text] and [Formula: see text] leads to numerical difficulties, namely the failure to allocate these matrices in certain memory-limited environments or excessive computational costs. Even though they do not possess any sparsity pattern, the Loewner and shifted Loewner matrices are extremely structured and, in this paper, we show how to fully exploit their Cauchy-like structure to reduce the cost of computing accurate rational models while avoiding the explicit allocation of [Formula: see text] and [Formula: see text] . In particular, the use of the hierarchically semiseparable format allows us to remarkably lower both the computational cost and the memory requirements of the Loewner framework obtaining a novel scheme whose costs scale with [Formula: see text]

Algorithm 854: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices II

This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stability as well as symmetry preservation for the computed eigenvalues. These algorithms are supplemented with balancing and block algorithms which can lead to considerable accuracy and performance improvements. As a by-product, an efficient implementation for computing symplectic QR decompositions is provided. We demonstrate the usefulness of the subroutines for several, practically relevant examples