Immersed Boundary Method for generalised finite volume and finite difference Navier-Stokes solvers

In Immersed Boundary Methods (IBM) the effect of complex geometries is introduced through the forces added in the Navier-Stokes solver at the grid points in the vicinity of the immersed boundaries. Most of the methods in the literature have been used with Cartesian grids. Moreover many of the methods developed in the literature do not satisfy some basic conservation properties (the conservation of torque, for instance) on non-uniform meshes. In this paper we will follow the RKPM method originated by Liu et al. [1] to build locally regularized functions that verify a number of integral conditions. These local approximants will be used both for interpolating the velocity field and for spreading the singular force field in the framework of a pressure correction scheme for the incompressible Navier-Stokes equations. We will also demonstrate the robustness and effectiveness of the scheme through various examples. Copyright © 2010 by ASME.

ZnO-Based FBAR resonators with carbon nanotube electrodes

Film bulk acoustic resonator (FBAR) devices with carbon nanotube (CNT) electrodes directly grown on a ZnO film by thermal chemical vapor deposition have been fabricated. CNT electrodes possess a very low density and high acoustic impedance, which reduces the intrinsic mass loading effect resulting from the electrodes' weight and better confines the longitudinal acoustic standing waves inside the resonator, in turn providing a resonator with a higher quality factor. The influence of the CNTs on the frequency response of the FBAR devices was studied by comparing two identical sets of devices; one set comprised FBARs fabricated with chromium/ gold bilayer electrodes, and the second set comprised FBARs fabricated with CNT electrodes. It was found that the CNTs had a significant effect on attenuating traveling waves at the surface of the FBARs' membranes because of their high elastic stiffness. Three-dimensional finite element analysis of the devices fabricated was carried out, and the numerical simulations were consistent with the experimental results obtained. © 2011 IEEE.

Simulated Annealing: Rigorous finite-time guarantees for optimization on continuous domains

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Finite element solution of Navier Stokes equations adapted to a priori error estimates

The paper is based on qualitative properties of the solution of the Navier-Stokes equations for incompressible fluid, and on properties of their finite element solution. In problems with corner-like singularities (e.g. on the well-known L-shaped domain) usually some adaptive strategy is used. In this paper we present an alternative approach. For flow problems on domains with corner singularities we use the a priori error estimates and asymptotic expansion of the solution to derive an algorithm for refining the mesh near the corner. It gives very precise solution in a cheap way. We present some numerical results.

Operating charts for the brushless doubly-fed machine (BDFM)

The Brushless Doubly-Fed Machine (BDFM) is an electrical machine that allows brushless operation in many applications where the Doubly-Fed Induction Generator (DFIG) is currently used. In recent years work on BDFM control means that the machine can now be run stably across its working range. However, little work has been done to define the working area in which BDFM can safely be operated without exceeding its material and stability limits. This paper sets out the theoretical backing for an operating chart of an ideal BDFM similar to that of the synchronous machine. It goes on to show that though the ideal chart gives the right form, non-ideal parameters (especially the finite magnetizing inductances) significantly effect the locations of the limits. Some preliminary experimental data obtained for a 225 frame size machine support the form of the chart. Finally it is shown how the operating chart can be used to chose appropriately sized converters for the BDFM. © 2009 IEEE.

Subdivision-stabilised immersed b-spline finite elements for moving boundary flows

An immersed finite element method is presented to compute flows with complex moving boundaries on a fixed Cartesian grid. The viscous, incompressible fluid flow equations are discretized with b-spline basis functions. The two-scale relation for b-splines is used to implement an elegant and efficient technique to satisfy the LBB condition. On non-grid-aligned fluid domains and at moving boundaries, the boundary conditions are enforced with a consistent penalty method as originally proposed by Nitsche. In addition, a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut-cells. The versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations.