High-order discontinuous Galerkin computation of axisymmetric transonic flows in safety relief valves

This paper presents a discontinuous Galerkin (DG) discretization of the compressible RANS and k–ω turbulence model equations for two-dimensional axisymmetric flows. The developed code has been applied to investigate the transonic flow in safety relief valves.This new DG implementation has evolved from the DG method presented in [1]. An “exact” Riemann solver is used to compute the interface numerical inviscid flux while the viscous flux discterization relies on the BRMPS scheme [2] and [3]. Control of oscillations of high-order solutions around shocks is obtained by means of a shock-capturing technique developed and assessed within the EU ADIGMA project [4].The code has been applied to compute the flow in a spring loaded safety valve at several back pressures and different disk lifts. The predicted device flow capacity and the pressure inside its bonnet have been checked against experimental data. The CFD simulations allow to clarify the complex flow patterns occurring and to explain the measured trends.     

Confronting intractability via parameters

One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are specified by their size alone. It is not hard to imagine that some parameters contribute more intractability than others and it seems reasonable to develop a theory of computational complexity which seeks to exploit this fact. Such a theory should be able to address the needs of practitioners in algorithmics. The last twenty years have seen the development of such a theory. This theory has a large number of successes in terms of a rich collection of algorithmic techniques, both practical and theoretical, and a fine-grained intractability theory. Whilst the theory has been widely used in a number of areas of applications including computational biology, linguistics, VLSI design, learning theory and many others, knowledge of the area is highly varied. We hope that this article will show the basic theory and point at the wide array of techniques available. Naturally the treatment is condensed, and the reader who wants more should go to the texts of Downey and Fellows (1999) [2], Flum and Grohe (2006) [59], Niedermeier (2006) [28], and the upcoming undergraduate text (Downey and Fellows 2012) [278].     

Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations

Asymptotic stability and boundedness have been two of most popular topics in the study of stochastic functional differential equations (SFDEs) (see e.g. Appleby and Reynolds (2008), Appleby and Rodkina (2009), Basin and Rodkina (2008), Khasminskii (1980), Mao (1995), Mao (1997), Mao (2007), Rodkina and Basin (2007), Shu, Lam, and Xu (2009), Yang, Gao, Lam, and Shi (2009), Yuan and Lygeros (2005) and Yuan and Lygeros (2006)). In general, the existing results on asymptotic stability and boundedness of SFDEs require (i) the coefficients of the SFDEs obey the local Lipschitz condition and the linear growth condition; (ii) the diffusion operator of the SFDEs acting on a C^2,1-function be bounded by a polynomial with the same order as the C^2,1-function. However, there are many SFDEs which do not obey the linear growth condition. Moreover, for such highly nonlinear SFDEs, the diffusion operator acting on a C^2,1-function is generally bounded by a polynomial with a higher order than the C^2,1-function. Hence the existing criteria on stability and boundedness for SFDEs are not applicable and we see the necessity to develop new criteria. Our main aim in this paper is to establish new criteria where the linear growth condition is no longer needed while the up-bound for the diffusion operator may take a much more general form.     

Mesoscale simulations of particulate flows with parallel distributed Lagrange multiplier technique

Fluid particulate flows are common phenomena in nature and industry. Modeling of such flows at micro and macro levels as well establishing relationships between these approaches are needed to understand properties of the particulate matter. We propose a computational technique based on the direct numerical simulation of the particulate flows. The numerical method is based on the distributed Lagrange multiplier technique following the ideas of Glowinski et al. [16] and Patankar [30]. Each particle is explicitly resolved on an Eulerian grid as a separate domain, using solid volume fractions. The fluid equations are solved through the entire computational domain, however, Lagrange multiplier constrains are applied inside the particle domain such that the fluid within any volume associated with a solid particle moves as an incompressible rigid body. Mutual forces for the fluid-particle interactions are internal to the system. Particles interact with the fluid via fluid dynamic equations, resulting in implicit fluid-rigid body coupling relations that produce realistic fluid flow around the particles (i.e., no-slip boundary conditions). The particle-particle interactions are implemented using explicit force-displacement interactions for frictional inelastic particles similar to the DEM method of Cundall et al. [10] with some modifications using a volume of an overlapping region as an input to the contact forces. The method is flexible enough to handle arbitrary particle shapes and size distributions. A parallel implementation of the method is based on the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) library, which allows handling of large amounts of rigid particles and enables local grid refinement. Accuracy and convergence of the presented method has been tested against known solutions for a falling particle as well as by examining fluid flows through stationary particle beds (periodic and cubic packing). To evaluate code performance and validate particle contact physics algorithm, we performed simulations of a representative experiment conducted at the U.C. Berkeley Thermal Hydraulic Lab for pebble flow through a narrow opening.     

Robust stability of interval time-delay systems with delay-dependence

This paper proposes a sufficient robust stability condition for interval time-delay systems with delay-dependence. The properties of the comparison theorem and matrix measure are employed to investigate the problem. The stability criteria are delay-dependent and less conservative than delay-independent stability criteria [5] , [6] , [12] and [16] and delay-dependent stability criteria 1, [14] , [15] and [17] when delay is small. However, the results of this paper indeed give us one more choice for the stability examination of the interval time-delay systems. Simulation examples are given to demonstrate the application of our result.     

Implicit methods for fluid dynamics

This paper represents the contributions to the development of implicit procedures for solving the equations of fluid dynamics made by Briley and McDonald (1975)[1], Beam and Warming (1976, 1978) [2] and [3] and Lombard et al. (1983) [4]. The contributions of Briley and McDonald and Beam and Warming are well known, but Lombard has not been fully recognized for his innovative contributions to flux vector splitting and use of the DDADI (Diagonally Dominate Alternating Direction Implicit) algorithm. Their contributions are presented herein.Fully implicit algorithms are applied to two complex flow problems of current interest, (1) hypersonic non-equilibrium flow about a blunt nosed body and (2) flow within an MFD (magneto-fluid dynamics) accelerator. These two applications would be exceeding costly without the use of fully implicit methods.     

Robust state estimation for uncertain discrete-time stochastic systems with missing measurements

In this paper, results of robust estimation of Zhou (2010a) are extended to state estimation with missing measurements. A new procedure is derived which inherits the main properties of that of Zhou (2010a). In this extension, a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult. Though introducing a monotonic function and using the so-called squeeze rule, this new robust estimator is proved to converge to a stable system. Numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of Wang, Yang, Daniel, and Liu (2005).     

A rational high-order compact ADI method for unsteady convection–diffusion equations

Based on a fourth-order compact difference formula for the spatial discretization, which is currently proposed for the one-dimensional (1D) steady convection–diffusion problem, and the Crank–Nicolson scheme for the time discretization, a rational high-order compact alternating direction implicit (ADI) method is developed for solving two-dimensional (2D) unsteady convection–diffusion problems. The method is unconditionally stable and second-order accurate in time and fourth-order accurate in space. The resulting scheme in each ADI computation step corresponds to a tridiagonal matrix equation which can be solved by the application of the 1D tridiagonal Thomas algorithm with a considerable saving in computing time. Three examples supporting our theoretical analysis are numerically solved. The present method not only shows higher accuracy and better phase and amplitude error properties than the standard second-order Peaceman–Rachford ADI method in Peaceman and Rachford (1959) [4], the fourth-order ADI method of Karaa and Zhang (2004) [5] and the fourth-order ADI method of Tian and Ge (2007) [23], but also proves more effective than the fourth-order Padé ADI method of You (2006) [6], in the aspect of computational cost. The method proposed for the diffusion–convection problems is easy to implement and can also be used to solve pure diffusion or pure convection problems.     

S-states of helium-like ions

A simple Mathematica (version 7) code for computing S-state energies and wave functions of two-electron (helium-like) ions is presented. The elegant technique derived from the classical papers of Pekeris (1958, 1959, 1962, 1965, 1971) [1], [2] and [3] is applied. The basis functions are composed of the Laguerre functions. The method is based on the perimetric coordinates and specific properties of the Laguerre polynomials. Direct solution of the generalized eigenvalues and eigenvectors problem is used, distinct from the Pekeris works. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of the results and computation times depend on the basis size. The ground state and the lowest triplet state energies can be computed with a precision of 12 and 14 significant figures, respectively. The accuracy of the higher excited states calculations is slightly worse. The resultant wave functions have a simple analytical form, that enables calculation of expectation values for arbitrary physical operators without any difficulties. Only three natural parameters are required in the input.The above Mathematica code is simpler than the earlier version (Liverts and Barnea, 2010 [4]). At the same time, it is faster and more accurate.

Program summary

Program title: TwoElAtomSL(SH)Catalogue identifier: AEHY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHY_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 11 434No. of bytes in distributed program, including test data, etc.: 540 063Distribution format: tar.gzProgramming language: Mathematica 7.0Computer: Any PCOperating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux SUSE 11.0RAM:?¹⁰⁹ bytesClassification: 2.1, 2.2, 2.7, 2.9Nature of problem: The Schrödinger equation for atoms (ions) with more than one electron has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or another physical attributes from quantum mechanical calculations.Solution method: The S-wave function is expanded into a triple set of basis functions which are composed of the exponentials combined with the Laguerre polynomials in the perimetric coordinates. Using specific properties of the Laguerre polynomials, solution of the two-electron Schrödinger equation reduces to solving the generalized eigenvalues and eigenvector problem for the proper Hamiltonian. The unknown exponential parameter is determined by means of minimization of the corresponding eigenvalue (energy).Restrictions: First, the too large length of expansion (basis size) takes the too large computation time and operative memory giving no perceptible improvement in accuracy. Second, the number of shells Ω in the wave function expansion enables one to calculate the excited nS-states up to n=Ω+1 inclusive.Running time: 2–60 minutes (depends on basis size and computer speed).     

Ideals with larger projective dimension and regularity

We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and improves upon constructions given by Caviglia (2004) and McCullough (2011). In particular, we describe a family of three-generated homogeneous ideals, in arbitrary characteristic, whose projective dimension grows asymptotically as a power of the degree of the generators.     

Large-eddy simulation in a complex hill terrain enabled by a compact fractional step OpenFOAM® solver

We report computational fluid dynamics (CFD) code developments using the high-level programming syntax of the open source C++ library OpenFOAM®. CFD simulations utilizing the large-eddy simulation (LES) approach are carried out using the developed code in a real-world application. We investigate wind flowing over the Bolund hill, Denmark. In the present configuration a west–east wind meets the steep west side of the hill. Such conditions lead to flow separation at the location of a sharp cliff. A full scale simulation, with a simulation duration of over one month, is carried out on a supercomputer. Physically, about 45 min of real time is simulated in the LES enabling the statistical averaging of the results. The novelty of the paper consists of the following features: (1) we report validation results of the newly developed LES code for the Bolund hill case, (2) we show the high-level LES solver code in its entirety in a few tens of code lines which promotes transparency in CFD-code development in the OpenFOAM® environment, (3) the study is the first study to use LES in pointing out the complex 3d characteristics of the Bolund hill case with the computationally challenging west–east (270°) wind direction, and (4) based on the comparison with previous experimental data, and Reynolds averaged Navier–Stokes (RANS) simulations, the present LES gives so far the best match for the turbulent kinetic energy increase at the considered measurement positions.     

Examining users’ preferences towards vertical graphical toolbars in simple search and point tasks

The main purpose of this study was to investigate the nature of preferences and their relation to the objective measures in simple direct manipulation tasks involving both the cognitive process as well as the visually guided pointing activities. The conducted experiment was concerned with the graphical structures resembling toolbars widely used in graphical interfaces. The influence of the graphical panel location, panel configuration as well as the target size on the user task efficiency and subjects’ preferences were examined. The participants were requested to express their attitudes towards the tested panels before and after the efficiency examination. This subjective evaluation was carried out within the framework of Analytic Hierarchy Process (AHP; Saaty, 1977, 1980). The subjective results that were obtained showed significant differences in the subjects’ preferences towards examined panels before and after completing the tasks. It seems that the users are able to comparatively quickly change their minds after gaining some experience with the investigated stimuli. Additionally, the applied cluster analysis revealed that the subjects were not homogenous in their opinions, and they formed groups having similar preference structures.     

Towards a three-dimensional moving body incompressible flow solver with a linear deformable model

In this study, a three-dimensional fluid–structured parallelized solver is extended from the previous work (Niu et al., 2009 [1]) for moving body simulations. Based on the unified Eulerian and Lagrangian coordinate transformations, the unsteady three-dimensional incompressible Navier–Stokes equations with artificial compressibility (Chorin, 1967 [2]) in a dual-time stepping approach are first derived. To implement unsteady flow calculations, the dual-time stepping strategy including the LU decomposition method is used in the pseudo-time iteration and the second-order accurate backward difference is adopted to discretize the unsteady flow terms. Also, a third-order Roe type flux limited splitting is derived to evaluate the spatial difference of the convective fluxes. The original FORTRAN code is converted to the MPI code and tested on a 64-CPU IBM SP2. The parallel strategy here is based on the partitions of all do-loops in the original FORTRAN code and transferring the calculations inside the do-loop into different CPUs. The partition of the do-loop can be applied on the innermost loop, only or the last two inner loops depending on two-dimensional or three-dimensional problems. This kind of the parallel data partition of the loops is independent of what kind of the explicit or implicit type numerical algorithm used. Therefore, the current parallel approach can take advantage of the MPI language fully to transfer data efficiently among CPUs even for solving the governing equation implicitly. The test results show that a significant reduction of computing time in running the model and a near-linear speed up rate is achieved up to 32 CPUs at IBM SP2. The speed up rate is as high as 31 for using 64 IBM SP2 processors The test shows efficient parallel processing to provide prompt simulation of 3D cavity, unsteady dropping airfoil and blood flows in an aortic tube with a linear elastic modeling of wall motion is included here.     

Convergence analysis of a class of simplified background neural networks with two subnetworks

Motivated by Salinas's (2003) original discovery in [1] and inspired by Oja's (1982) seminal work in [2], in this paper, we propose a class of simplified background neural networks model with two subnetworks. Some basic dynamic properties including boundedness, global attractivity, stability, and complete convergence are analyzed rigorously. The main contributions in this paper are as follows: (1) The boundedness of the new model is verified and conditions for global attractivity are derived. (2) Conditions on asymptotically stable of equilibrium points are obtained. (3) Complete convergence for the new network is proved by constructing a novel energy function. Finally, numerical examples demonstrate our theoretical results.     

Cooperative strategies of wireless access technologies: A game-theoretic analysis

The wireless Internet has to overcome the problem of spectrum scarcity as the number of mobile equipments could increase even by an order of magnitude in the next decade; the cooperation of mobile devices is foreseeable as a feasible solution to the problems. There exists a large body of literature on opportunistic ad hoc networking including Pelusi et al. (2006) [25], Chen et al. (2006) [26], Hui et al. (2005) [27]; however, the impact of the location of the devices on their access method selection is not yet appropriately dealt with. In this paper, we address this issue based on game-theoretic analyses. The key contribution of our work is threefold. First, we model the access method selection of mobile devices by extending the classical forwarding game with position, mobility, and availability of the devices. Second, we apply the model in game-theoretic analyses to better understand the optimal cooperation strategies in the presence of heterogeneous wireless technologies. We further extend our framework to include uncertainty. Finally, we present the applicability of the model in a cognitive radio scenario where complex structures of parameters are included.     

Algorithms for computing a primary ideal decomposition without producing intermediate redundant components

In Noro (2010) we proposed an algorithm for computing a primary ideal decomposition by using the notion of a separating ideal and showed that it can efficiently decompose several examples which are hard to decompose using existing algorithms. In particular, the number of redundant components produced in the algorithm is zero or very small in many examples, but no theoretical explanation for the efficiency was given.In this paper we define a more sophisticated class of separating ideals: saturated separating ideals. By using this notion we modify the algorithm of Noro (2010) such that it directly outputs a minimal primary decomposition without producing any intermediate redundant component.By modifying the process of extraction of a primary component via the pseudo-primary decomposition proposed in Shimoyama and Yokoyama (1996), we find a method for intermediate decomposition of an ideal and propose a variant of the new primary decomposition algorithm based on this intermediate decomposition. Our experiment shows that this variant efficiently decomposes many examples which are still hard to decompose even if we apply the original version of the new algorithm. Furthermore, in this algorithm we can bypass the computation of primary components and obtain directly the set of all associated primes of an ideal.     

Can the uncertainty in brass casting blending problem be managed? A probability/possibility transformation approach

Problems about the uncertainty in raw material compositions are a critical issue for the blending problems. It is feared that uncertainty in raw material compositions would often cause percent values of the actual blend to go out of specification limits. In this paper, the aleatory and epistemic uncertainties have been handled simultaneously in a blending optimization problem for brass casting. The aleatory and epistemic uncertainties are modeled by using probability and possibility theories respectively. However, the probabilistic and the possibilistic uncertainties are different from the each other. Therefore to solve the mathematical model, including these uncertainties, a transformation of any type of uncertainty to the other is needed. In this study, probabilistic uncertainties are transformed to the possibilistic uncertainties by considering Rong and Lahdelma’s (2008) and the Dubois, Prade, and Sandri (1993) and Dubois, Foulloy, Mauris, and Prade (2004) transformation approaches. This transformation process converts the former model to a possibilistic model. Then the possibilistic models, obtained from each transformation, are solved by using α cuts approach. The solutions of the two possibilistic models have shown that the model, which uses Dubois’s transformation, prepares blends with lower cost than the other model, which uses Rong and Lahdelma’s transformation.     

Nonlinear dynamic allocator for optimal input/output performance trade-off: Application to the JET tokamak shape controller

In this paper, we revisit the dynamic allocation scheme for input redundant plants proposed in Zaccarian (2009). within a set-point regulation setting and propose generalizations that apply to cases where the plant under consideration is not input redundant but the control specifications allow us to modify the set-point regulation within certain bounds. In this case, the input allocator is extended to the nonredundant case by allowing it to improve the input allocation selection at the price of some output regulation error. We also establish here desirable convergence properties of the allocator, which were only addressed for the linear case in Zaccarian (2009). In particular, we design the allocator dynamics as the gradient of a cost function and establish its convergence to the minimum of the cost function under some mild conditions. The allocation scheme is applied to the JET tokamak shape controller by illustrating its capabilities to enforce coil currents selections that tend to move away from the saturation limits within the allowable degrees of freedom.     

Automated quantum conductance calculations using maximally-localised Wannier functions

A robust, user-friendly, and automated method to determine quantum conductance in quasi-one-dimensional systems is presented. The scheme relies upon an initial density-functional theory calculation in a specific geometry after which the ground-state eigenfunctions are transformed to a maximally-localised Wannier function (MLWF) basis. In this basis, our novel algorithms manipulate and partition the Hamiltonian for the calculation of coherent electronic transport properties within the Landauer–Buttiker formalism. Furthermore, we describe how short-ranged Hamiltonians in the MLWF basis can be combined to build model Hamiltonians of large (>10,000 atom) disordered systems without loss of accuracy. These automated algorithms have been implemented in the Wannier90 code (Mostofi et al., 2008) [1], which is interfaced to a number of electronic structure codes such as Quantum-ESPRESSO, AbInit, Wien2k, SIESTA and FLEUR. We apply our methods to an Al atomic chain with a Na defect, an axially heterostructured Si/Ge nanowire and to a spin-polarised defect on a zigzag graphene nanoribbon.