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.     

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.     

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.     

Improved parallelized hybrid DSMC–NS method

In this paper, an improved parallelized hybrid DSMC–NS (Navier–Stokes method) algorithm, as compared to the previous work [1], is presented. A detailed kinetic velocity sampling study is conducted with a two-dimensional supersonic flow (M_∞ = 4) past a 25° finite wedge. It shows most of the boundary layer region is in nearly thermal equilibrium, even with very high continuum breakdown parameter based on velocity, velocity gradient and local mean free path. A new continuum breakdown parameter based on pressure is designed to effectively “exclude” the “false” breakdown region such as the boundary layer. An improved hybrid DSMC–NS algorithm is verified using the same wedge flow case. Results show that the improved algorithm can greatly reduce the computational cost while maintaining essentially the same accuracy. A hypersonic flow (M_∞ = 12) past a square cylinder is also employed to exhibit the capability of the improved hybrid DSMC–NS method.     

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.     

An implicit MacCormack scheme for unsteady flow calculations

This paper describes the implicit MacCormack scheme [1] in finite volume formulation. Unsteady flows with moving boundaries are considered using arbitrary Lagrangian–Eulerian approach.The scheme is unconditionally stable and does not require solution of large systems of linear equations. Moreover, the upgrade from explicit MacCormack scheme to implicit one is very simple and straightforward.Several computational results for 2D and 3D flows over profiles and wings are presented for the case of inviscid and viscous flows.     

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].     

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.     

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).     

A spectral collocation method for a rotating Bose–Einstein condensation in optical lattices

We extend the study of spectral collocation methods (SCM) in Li et al. (2009) [1] for semilinear elliptic eigenvalue problems to that for a rotating Bose–Einstein condensation (BEC) and a rotating BEC in optical lattices. We apply the Lagrange interpolants using the Legendre–Gauss–Lobatto points to derive error bounds for the SCM. The optimal error bounds are derived for both H¹-norm and L²-norm. Extensive numerical experiments on a rotating Bose–Einstein condensation and a rotating BEC in optical lattices are reported. Our numerical results show that the convergence rate of the SCM is exponential, and is independent of the collocation points we choose.     

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.     

Memory lower bounds for XPath evaluation over XML streams

We consider the XPath evaluation problem: Evaluate an XPath query Q on a streaming XML document D. We consider two versions of the problem: 1) Filtering Problem: Determine if there is a match for Q in D. 2) Node Selection Problem: Determine the set Q(D) of document nodes selected by Q. We consider Conjunctive XPath (CXPath) queries that involve only the child and descendant axes. Let d denote the depth of D, and n denote the number of location steps in Q. Bar-Yossef et al. (2007, 2005) [6] and [7] presented lower bounds on the memory space required by any algorithm to solve these two problems. Their lower bounds apply to each query in a large subset of XPath, and are obtained (mostly) using nonrecursive(Q,D). In this paper, we present larger lower bounds for a different class of queries (namely, CXPath queries with independent predicates), on recursive(Q,D). One of our results is an Ω(n⋅maxcands(Q,D)) lower bound for the node selection problem, for a worst-case Q; maxcands(Q,D) is the maximum number of nodes of D that can be candidates for output, at any one instant. So, there is no algorithm for the node selection problem that uses O(f(d,|Q|)+maxcands(Q,D)) space, for any function f. This shows that some previously published algorithms are incorrect.     

Improvements of the particle-in-cell code EUTERPE for petascaling machines

In the present work we report some performance measures and computational improvements recently carried out using the gyrokinetic code EUTERPE (Jost, 2000 [1] and Jost et al., 1999 [2]), which is based on the general particle-in-cell (PIC) method. The scalability of the code has been studied for up to sixty thousand processing elements and some steps towards a complete hybridization of the code were made. As a numerical example, non-linear simulations of Ion Temperature Gradient (ITG) instabilities have been carried out in screw-pinch geometry and the results are compared with earlier works. A parametric study of the influence of variables (step size of the time integrator, number of markers, grid size) on the quality of the simulation is presented.     

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.     

Propagation of gravity waves through an SPH scheme with numerical diffusive terms

Basing on the work by Antuono et al. (2010) [1], an SPH model with numerical diffusive terms (here denoted δ-SPH) is combined with an enhanced treatment of solid boundaries to simulate 2D gravity waves generated by a wave maker and propagating into a basin. Both regular and transient wave systems are considered. In the former, a large number of simulations is performed for different wave steepness and height-to-depth ratio and the results are compared with a BEM Mixed-Eulerian–Lagrangian solver (here denoted BEM-MEL solver). In the latter, the δ-SPH model has been compared with both the experimental measurements available in the literature and with the BEM-MEL solver, at least until the breaking event occurs. The results show a satisfactory agreement between the δ-SPH model, the BEM-MEL solver and the experiments. Finally, the influence of the weakly-compressibility assumption on the SPH results is inspected and a convergence analysis is provided in order to identify the minimal spatial resolution needed to get an accurate representation of gravity waves.     

B-spline surface fitting based on adaptive knot placement using dominant columns

By expanding the idea of B-spline curve fitting using dominant points (Park and Lee 2007 [13]), we propose a new approach to B-spline surface fitting to rectangular grid points, which is based on adaptive knot placement using dominant columns along u- and v-directions. The approach basically takes approximate B-spline surface lofting which performs adaptive multiple B-spline curve fitting along and across rows of the grid points to construct a resulting B-spline surface. In multiple B-spline curve fitting, rows of points are fitted by compatible B-spline curves with a common knot vector whose knots are computed by averaging the parameter values of dominant columns selected from the points. We address how to select dominant columns which play a key role in realizing adaptive knot placement and thereby yielding better surface fitting. Some examples demonstrate the usefulness and quality of the proposed approach.     

Partial enumeration MPC: Robust stability results and application to an unstable CSTR

We describe a partial enumeration (PE) method for fast computation of a suboptimal solution to linear MPC problems [1] with robust stability properties. Given that the suboptimal PE-based control law is non-unique (that is, a set-valued map) and (possibly) discontinuous, we treat the closed-loop system, appropriately augmented, as a difference inclusion. We derive novel robust exponential stability results for difference inclusions of this type. In particular we show that Strong Robust Exponential Stability (SRES) holds, for any sufficiently small but otherwise arbitrary perturbation. Such approach allows us to show SRES of the closed-loop system under PE-based MPC. Application to a simulated open-loop unstable CSTR with separation unit and recycle is presented to show performance and timing results for PE-based MPC, as well as to highlight its robustness to process/model mismatch, disturbances and measurement noise.     

Comparison of two numerical methods for the stratified flow

The article is devoted to numerical simulation of stratified flows described by the Navier-Stokes equations in Boussinesq approximation. The equations are solved by two high order schemes. The first one using the fifth-order WENO scheme combined with spectral projection to solenoidal field, the second one being based on the second-order AUSM MUSCL scheme with artificial compressibility in dual time.The schemes are used to model a flow around an obstacle moving through the stratified fluid. The setup of the computational case corresponds to the experiment of Chaschechkin and Mitkin [23]. Mutual comparison of results obtained by both schemes as well as of the experimental data is presented.     

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.