Physics based GMRES preconditioner for compressible and incompressible Navier-Stokes equations

This paper presents the implementation of a local physics preconditioning mass matrix [8] for an unified approach of 3D compressible and incompressible Navier-Stokes equations using an SUPG finite element formulation and GMRES implicit solver. During the last years a lot of effort has been dedicated to finding a unified approach for compressible and incompressible flow in order to treat fluid dynamic problems with a very wide range of Mach and Reynolds numbers [10,26,37]. On the other hand, SUPG finite element formulation and GMRES implicit solver is one of the most robust combinations to solve state of the art CFD problems [1,6,9,22,29,30,31]. The selection of a good preconditioner and its performance on parallel architecture is another open problem in CFD community. The local feature of the preconditioner presented here means that no communication among processors is needed when working on parallel architectures. Due to these facts we consider that this research can make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of Mach and Reynolds numbers, being very suitable for massively parallel computations. Finally, it is important to remark that while this kind of preconditioning produces stabilized results in nearly incompressible regimes the standard version exhibits some numerical drawbacks that lead to solutions without physical meaning

Bogoliubov modes of a dipolar condensate in a cylindrical trap

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation

MODEL UPDATING AND STRUCTURAL HEALTH MONITORING OF HORIZONTAL AXIS WIND TURBINES VIA ADVANCED SPINNING FINITE ELEMENTS AND STOCHASTIC SUBSPACE IDENTIFICATION METHODS

Wind energy has been one of the most growing sectors of the nation’s renewable energy portfolio for the past decade, and the same tendency is being projected for the upcoming years given the aggressive governmental policies for the reduction of fossil fuel dependency. Great technological expectation and outstanding commercial penetration has shown the so called Horizontal Axis Wind Turbines (HAWT) technologies. Given its great acceptance, size evolution of wind turbines over time has increased exponentially. However, safety and economical concerns have emerged as a result of the newly design tendencies for massive scale wind turbine structures presenting high slenderness ratios and complex shapes, typically located in remote areas (e.g. offshore wind farms). In this regard, safety operation requires not only having first-hand information regarding actual structural dynamic conditions under aerodynamic action, but also a deep understanding of the environmental factors in which these multibody rotating structures operate. Given the cyclo-stochastic patterns of the wind loading exerting pressure on a HAWT, a probabilistic framework is appropriate to characterize the risk of failure in terms of resistance and serviceability conditions, at any given time. Furthermore, sources of uncertainty such as material imperfections, buffeting and flutter, aeroelastic damping, gyroscopic effects, turbulence, among others, have pleaded for the use of a more sophisticated mathematical framework that could properly handle all these sources of indetermination. The attainable modeling complexity that arises as a result of these characterizations demands a data-driven experimental validation methodology to calibrate and corroborate the model. For this aim, System Identification (SI) techniques offer a spectrum of well-established numerical methods appropriated for stationary, deterministic, and data-driven numerical schemes, capable of predicting actual dynamic states (eigenrealizations) of traditional time-invariant dynamic systems. As a consequence, it is proposed a modified data-driven SI metric based on the so called Subspace Realization Theory, now adapted for stochastic non-stationary and timevarying systems, as is the case of HAWT’s complex aerodynamics. Simultaneously, this investigation explores the characterization of the turbine loading and response envelopes for critical failure modes of the structural components the wind turbine is made of. In the long run, both aerodynamic framework (theoretical model) and system identification (experimental model) will be merged in a numerical engine formulated as a search algorithm for model updating, also known as Adaptive Simulated Annealing (ASA) process. This iterative engine is based on a set of function minimizations computed by a metric called Modal Assurance Criterion (MAC). In summary, the Thesis is composed of four major parts: (1) development of an analytical aerodynamic framework that predicts interacted wind-structure stochastic loads on wind turbine components; (2) development of a novel tapered-swept-corved Spinning Finite Element (SFE) that includes dampedgyroscopic effects and axial-flexural-torsional coupling; (3) a novel data-driven structural health monitoring (SHM) algorithm via stochastic subspace identification methods; and (4) a numerical search (optimization) engine based on ASA and MAC capable of updating the SFE aerodynamic model

Reduced-order modelling and feedback control of integrally actuated membrane wings

This paper presents a numerical investigation on aerodynamic control of integrally-actuated membrane wings made of dielectric elastomers. They combine the advantages of membrane shape adaptability with the benefits of the simple, lightweight but high-authority control mechanism offered by integral actuation. For that purpose, high-fidelity numerical models have been developed to predict their performance. They include a fluid solver based on the direct numerical integration of the unsteady Navier-Stokes equations, an electromechanical constitutive material model and a non-linear three-dimensional membrane structural model. In addition, using the Eigensystem Realization Algorithm, it is obtained a very low order model description of the fully coupled aero-electromechanical system to aid the design of a simple PID control scheme for the feedback control of the wing. The resulting regulator is then implemented in the high-fidelity model and used for the mitigation of flow disturbances

Component Mode Synthesis Approach for Quantum Mechanical Electrostatic and Transport Analysis of Nanoscale Structures and Devices

As the dimensions of commonly used semiconductor devices have shrunk into nanometer regime, it is recognized that the influence of quantum effects on their electrostatic and transport properties cannot be ignored. In the past few decades, various computational models and approaches have been developed to analyze these properties in nanostructures and devices. Among these computational models, the Schršdinger-Poisson model has been widely adopted for quantum mechanical electrostatic and transport analysis of nanostructures and devices such as quantum wires, metal-oxide-semiconductor field effect transistors (MOSFETs) and nanoelectromechanical systems (NEMS). The numerical results allow for evaluations of the electrical properties such as charge concentration and potential profile in these structures. The emergence of MOSFETs with multiple gates, such as Trigates, FinFETs and Pi-gates, offers a superior electrostatic control of devices by the gates, which can be therefore used to reduce the short channel effects within those devices. Full 2-D electrostatic and transport analysis enables a better understanding of the scalability of devices, geometric effects on the potential and charge distribution, and transport characteristics of the transistors. The Schršdinger-Poisson model is attractive due to its simplicity and straightforward implementation by using standard numerical methods. However, as it is required to solve a generalized eigenvalue problem generated from the discretization of the Schršdinger equation, the computational cost of the analysis increases quickly when the system\u27s degrees of freedom (DOFs) increase. For this reason, techniques that enable an efficient solution of discretized Schršdinger equation in multidimensional domains are desirable. In this work, we seek to accelerate the numerical solution of the Schršdinger equation by using a component mode synthesis (CMS) approach. In the CMS approach, a nanostructure is divided into a set of substructures or components and the eigenvalues (energy levels) and eigenvectors (wave functions) are computed first for all the substructures. The computed wave functions are then combined with constraint or attachment modes to construct a transformation matrix. By using the transformation matrix, a reduced-order system of the Schršdinger equation is obtained for the entire nanostructure. The global energy levels and wave functions can be obtained with the reduced-order system. Through an iteration procedure between the Schršdinger and Poisson equations, a self-consistent solution for charge concentration and potential profile can be obtained. In this work, the CMS approach is applied to compute the electrostatic and transport properties of a set of semiconductor devices including a quantum wire and several multiple-gate MOSFETs. It is demonstrated that the CMS approach greatly reduces the computational cost while giving accurate results

Parallel eigenanalysis of finite element models in a completely connected architecture

A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi) = (M)(phi)(omega), where (K) and (M) are of order N, and (omega) is order of q. The concurrent solution of the eigenproblem is based on the multifrontal/modified subspace method and is achieved in a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm was successfully implemented on a tightly coupled multiple-instruction multiple-data parallel processing machine, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macrotasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. A parallel finite element dynamic analysis program, p-feda, is documented and the performance of its subroutines in parallel environment is analyzed