Simulating flows with moving rigid boundary using immersed-boundary method

The present study is to apply the immersed-boundary method to simulate 2- and 3-D viscous incompressible flows interacting with moving solid boundaries. Previous studies indicated that for stationary-boundary problems, different treatments inside the solid body did not affect the external flow. However, the relationship between internal treatment of the solid body and external flow for moving-boundary problems was not studied extensively and is investigated here. This is achieved via direct-momentum forcing on a Cartesian grid by combining “solid-body forcing” at solid nodes and interpolation on neighboring fluid nodes. The influence of the solid body forcing within the solid nodes is first examined by computing flow induced by an oscillating cylinder in a stationary square domain, where significantly lower amplitude oscillations in computed lift and drag coefficients are obtained compared with those without solid-body-forcing strategy. Grid-function convergence tests also indicate second-order accuracy of this implementation with respect to the L¹ norm in time and the L² norm in space. Further test problems are simulated to examine the validity of the present technique: 2-D flows over an asymmetrically-placed cylinder in a channel, in-line oscillating cylinder in a fluid at rest, in-line oscillating cylinder in a free stream, two cylinders moving with respect to one another, and 3-D simulation of a sphere settling under gravity in a static fluid. All computed results are in generally good agreement with various experimental measurements and with previous numerical simulations. This indicates the capability of the present simple implementation in solving complex-geometry flow problems and the importance of solid body forcing in computing flows with moving solid objects.     

Parallel Computation and Indefinite Summation: a MAPLE Application for the Rational Case

The problem of computing a closed form for sums of special functions arises in many parts of mathematical and computer science, especially in combinatorics and complexity analysis. Here we discuss two algorithms for indefinite summation of rational functions, due to Abramov (1975) and Paule (1993). We describe some improvements and a parallel implementation on a workstation network in MAPLE (read: parallel Maple). Our best implementation achieves a speedup of up to eight over the fastest available sequential implementation. Finally, further applications of parallel computing in this field are outlined.     

Space-time discretizing optimal DRP schemes for flow and wave propagation problems

The present paper reports constrained optimization of explicit Runge–Kutta (RK) schemes, coupled with optimal upwind compact scheme to achieve dispersion relation preservation (DRP) property for high performance computing. Essential ideas of optimization employed in arriving at the proposed time integration scheme are extension of the earlier work reported in Rajpoot et al. (J Comput Phys 2010;229:3623–51). This is in turn an application of the correct error evolution equation in Sengupta et al. (J Comput Phys 2007;226:1211–8). Resultant DRP scheme demonstrated the idea for explicit spatial central difference schemes. Present work is similar, extending it for near-spectral accuracy compact schemes. Practical utility of the developed method is demonstrated by solution of model problems and for flow problems by solving Navier–Stokes equation, some of which cannot be solved by conventional schemes, as the problem of rotary oscillation of cylinder.Developed method is calibrated with: (i) flow past a circular cylinder performing rotary oscillation at Re = 150 and (ii) flow inside a 2D lid-driven cavity (LDC) at Reynolds numbers of Re = 1000 and Re = 10,000. Quantitative and qualitative comparisons show excellent match for rotary oscillation cylinder cases with the experimental results of Thiria et al. (J Fluid Mech 2006;560:123–47). Results for LDC for Re = 1000 are compared with that in Botella & Peyret (Comp Fluids 1998;27:421–33) and results for Re = 10,000 are compared with recent published ones showing triangular vortex in the core.     

Numerical analysis and computations of a high accuracy time relaxation fluid flow model

We present a numerical study based on continuous finite element analysis for a time relaxation regularization of Navier–Stokes equations. This regularization is based on filtering and deconvolution. We study the convergence of the regularized equations using a fully discretized filter and deconvolution algorithm. Velocity and pressure error estimates and the L ₂ Aubin–Nitsche lift technique are proved for the equilibrium problem, and this analysis is accompanied by the velocity error estimate for the time-dependent problem, too. Thus, optimal error estimates in L ₂ and H ¹ norms are derived and followed by their computational verification. Also, computational results of the vortex street are presented for the two-dimensional cylinder benchmark flow problem. Maximum drag and lift coefficients and difference in pressure between the front and back of the cylinder at the final time were investigated as well, showing that the time relaxation regularization can attain the benchmark values.     

Computer algebra tailored to matrix inequalities in control

A major advance in linear systems theory over the last decade has been a formalism for converting systems problems to matrix inequalities. In this tutorial paper we describe computer algebra algorithms, methodology, and implementation which allows users to convert many systems problems to linear matrix inequalities (LMIs). We shall focus on computer algebra methodology which can assist the user in producing LMIs for control design. We provide a step-by-step computer derivation of LMI formulas for the design of linear time-invariant dynamic controllers that achieve a prespecified performance measured by the H _∞ norm of a certain closed loop transfer function.     

A Parallel Overset Grid High-Order Flow Solver for Large Eddy Simulation

This work describes the development and validation of a parallel high-order compact finite difference Navier–Stokes solver for application to large-eddy simulation (LES) and direct numerical simulation. The implicit solver can employ up to sixth-order spatial formulations and tenth-order filtering. The parallelization of the solver is founded on the overset grid technique. LES were then performed for turbulent channel flow with Reynolds numbers ranging from Re _τ=180 to 590, and flow past a circular cylinder with a transitional wake at Re _D =3900. The channel flow solutions were obtained using both an implicit LES (ILES) approach and a dynamic sub-grid scale model. The ILES method obtained virtually identical solutions at half the computational cost. The original vector and new parallel solvers produce indistinguishable mean flow solutions for the circular cylinder. Repeating the cylinder simulation on a much finer mesh resulted in significantly better agreement with experimental data in the near wake than the coarse grid solution and other previous numerical studies.     

Experimental demonstration of non-local controlled-unitary quantum gates using a five-qubit quantum computer

Local implementation of non-local quantum gates is necessary in a distributed quantum computer. Here, we demonstrate the non-local implementation of controlled-unitary quantum gates proposed by Eisert et al. (Phys Rev A 62:052317, 2000) using the five-qubit IBM quantum computer. We verify the fidelity and accuracy of the implementation through the techniques of quantum state and process tomographies.     

Parallel solution of dense linear systems using diagonalization methods

We study the parallel implementation of two diagonalization methods for solving dense linear systems: the well known Gauss-Jordan method and a new one introduced by Huard. The number of arithmetic operations performed by the Huard method is the same as for Gaussian elimination, namely 2n ³/3, less than for the Jordan method, namely n ³. We introduce parallel versions of these methods, compare their performances and study their complexity. We assume a shared memory computer with a number of processors p of the order of n, the size of the problem to be solved, We show that the best parallel version for Jordan's method is by rows whereas the best one for Huard's method is by columns. Our main result states that for a small number of processors the parallel Huard method is faster than the parallel Jordan method and slower otherwise. The separation is obtained for p = 0.44n.     

Attentional Scene Segmentation: Integrating Depth and Motion

We present an approach to attention in active computer vision. The notion of attention plays an important role in biological vision. In recent years, and especially with the emerging interest in active vision, computer vision researchers have been increasingly concerned with attentional mechanisms as well. The basic principles behind these efforts are greatly influenced by psychophysical research. That is the case also in the work presented here, which adapts to the model of Treisman (1985, Comput. Vision Graphics Image Process. Image Understanding31, 156–177), with an early parallel stage with preattentive cues followed by a later serial stage where the cues are integrated. The contributions in our approach are (i) the incorporation of depth information from stereopsis, (ii) the simple implementation of low level modules such as disparity and flow by local phase, and (iii) the cue integration along pursuit and saccade mode that allows us a proper target selection based on nearness and motion. We demonstrate the technique by experiments in which a moving observer selectively masks out different moving objects in real scenes.     

Multi-objective optimization of the heat transmission and fluid forces around a rounded cornered square cylinder

The unsteady fluid stream and warmth transmission nearby a square cylinder with sharp and rounded cornered edges are numerically examined, and then the roundness of the corner is predicted and optimized for the minimum fluid forces and maximum heat transmission rate. The roundness of the cylinder corner is changing 0.5D (circle) to 0.71D (square); D is the depth of the cylinder. The fluid flow and the heat transmission features around the sharp and curved cornered square cylinder are evaluated with the streamline, isotherm patterns, pressure coefficient, drag and lift coefficients, local Nusselt number (Nu_local) and average Nusselt number (Nu_avg) at different Re and for several roundness values. These characteristics are predicted by the gene expression programming, and then the multi-objective genetic algorithm is utilized for the optimization. A number of combinations of values of corners have been found in the form of Pareto-optimal solution to compromise the minimum fluid forces with maximum heat transfer rate.

     

Effect of internal mass in the simulation of a moving body by the immersed boundary method

We investigate the effect of internal mass in the simulation of a moving body by the immersed boundary method. In general, the force and the torque acting on the body are influenced by the internal mass, if they are obtained by the negative of the sum of body forces which are applied near the boundary in order to enforce the no-slip condition on the boundary. In this study, the following schemes for approximating the internal mass effect are introduced; no internal mass effect, rigid body approximation, and Lagrangian points approximation. By comparing these schemes through the simulations of a moving body, we examine the internal mass effect. The simulations of the flow around an oscillating circular cylinder and of the sedimentations of an elliptical cylinder and a sphere are performed by using an immersed boundary–lattice Boltzmann method, and it is found that the internal mass effect is significant to unsteady body motions for the Reynolds numbers over 10 and grows as the Reynolds number increases. We also find that for the angular motions of the body, the rigid body approximation causes errors for the rotational Reynolds numbers over 10.     

Vega: Non‐Linear FEM Deformable Object Simulator

This practice and experience paper describes a robust C++ implementation of several non‐linear solid three‐dimensional deformable object strategies commonly employed in computer graphics, named the Vega finite element method (FEM) simulation library. Deformable models supported include co‐rotational linear FEM elasticity, Saint–Venant Kirchhoff FEM model, mass–spring system and invertible FEM models: neo‐Hookean, Saint–Venant Kirchhoff and Mooney–Rivlin. We provide several timestepping schemes, including implicit Newmark and backward Euler integrators, and explicit central differences. The implementation of material models is separated from integration, which makes it possible to employ our code not only for simulation, but also for deformable object control and shape modelling. We extensively compare the different material models and timestepping schemes. We provide practical experience and insight gained while using our code in several computer animation and simulation research projects.     

NGluon: A package to calculate one-loop multi-gluon amplitudes

We present a computer library for the numerical evaluation of colour-ordered n-gluon amplitudes at one-loop order in pure Yang–Mills theory. The library uses the recently developed technique of generalised unitarity. Running in double precision the library yields reliable results for up to 14 gluons with only a small fraction of events requiring a re-evaluation using extended floating point arithmetic. We believe that the library presented here provides an important contribution to future LHC phenomenology. The program may also prove useful in cross checking results obtained by other methods. In addition, the code provides a sample implementation which may serve as a starting point for further developments.

Program summary

Program title:NGluonCatalogue identifier: AEIZ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIZ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: GNU Public LicenseNo. of lines in distributed program, including test data, etc.: 30 677No. of bytes in distributed program, including test data, etc.: 334 896Distribution format: tar.gzProgramming language: C++Computer: Any computer platform supported by the GNU compiler suite.Operating system: No specific requirements – tested on Scientific Linux 5.2.RAM: Depending on the complexity, for realistic applications like 10 gluon production in double precision below 10 MB.Classification: 11.5External routines: QCDLoop (http://qcdloop.fnal.gov/), qd (http://crd.lbl.gov/~dhbailey/mpdist/)Nature of problem: Evaluation of next-to-leading order corrections for gluon scattering amplitudes in pure gauge theory.Solution method: Purely numerical approach based on tree amplitudes obtained via Berends–Giele recursion combined with unitarity method.Restrictions: Running in double precision the number of gluons should not exceed 14.Running time: Depending on the number of external gluons between less than a millisecond (4 gluons) up to a 1 s (14 gluons) per phase space point.     

Analogue algorithm for parallel factorization of an exponential number of large integers: I. Theoretical description

We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of “factoring” interferograms measured at the output of an analogue computer that allows the selection of the factors of each integer. At the present stage, the algorithm manifests an exponential scaling which may be overcome by an extension of this method to correlated qubits emerging from n-order quantum correlations measurements. We describe the conditions for a generic physical system to compute such an analogue algorithm. A particular example given by an “optical computer” based on optical interference will be addressed in the second paper of this series (Tamma in Quantum Inf Process 11128:1189, 2015).

     

Single-layer cylindrical compaction

In VLSI compaction, an array composed of a single cell warrants special consideration. Standard methods of compaction [MS] result in either nonuniform cell layouts or unnecessarily large cell spacing. These inadequacies would be lessened were the array compacted instead by compacting a single instance of the cell against itself: in essence, the cell would be compacted on a torus. Equivalently, the problem becomes that of compacting a layout to fit into a minimal area shape 4-tiling the plane.Only the one-dimensional version of the problem has been addressed: that equivalent to compaction on a cylinder. Unfortunately, the efficient longest-path approach to one-dimensional compaction is not directly applicable since there is no origin to compact against. Eichenberger and Horowitz solve the problem in polynomial time by using a min-cost flow approach to assign positions to the nodes of a constraint network embedded on a cylinder [EH]. Mehlhorn and Rülling found an iterative approach running in timeO(n ² logn) when restricted to networks abstracted from layouts having any fixed number of layers [MR]. In this paper the longest-path approach is adapted to solve the same cylindrical compaction problem on planar networks—those abstracted from single-layer layouts—in justO(n logn) time.This research was supported by NSF Presidential Young Investigator Grant MIP-8657693.     

Pore scale definition and computation from tomography data

During recent years characterisation capabilities of porous media have been transformed by advances in computation and visualisation technologies. It is now possible to obtain detailed topological and hydrodynamic information of porous media by combining tomographic and computational fluid dynamic studies. Despite the existence of these new capabilities, the characterisation process itself is based on the same antiquated experimental macroscopic concepts.We are interested in an up-scaling process where we can keep key information for every pore size present in the media in order to feed multi-scale transport models. Hydrometallurgical, environmental, food, pharmaceutical and chemical engineering are industries with process outcomes based on homogeneous and heterogeneous reactions and therefore sensitive to the reaction and transport processes happening at different pore scales.The present work addresses a key step in the information up-scaling process, i.e. a pore identification algorithm similar to alternating sequential filters. In a preliminary study, topological and hydrodynamic variables are correlated with the pore size. Micrometre and millimetre resolution tomographies are used to characterise the pore size distribution of a packed column and different rocks. Finally, we compute the inter-pore-scale redistribution function which is a measure of the heterogeneity of the media and magnitude needed in multi-scale modelling.

Program summary

Program title: PoresizedistCatalogue identifier: AEJJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJJ_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.: 312No. of bytes in distributed program, including test data, etc.: 6534Distribution format: tar.gzProgramming language: MatLabComputer: Desktop or LaptopOperating system: Runs under MatLab (tested in Linux and Windows)RAM: Tested for problems up to 10¹⁰ bytesClassification: 7.9, 14External routines: MatLab Image ToolboxNature of problem: Identify individual pores from a foreground image representing void space.Solution method: Algorithm based on successive erosions with a shrinking erosion disk diameter.Restrictions: The tomographic data must fit in the available computer memory. The input tomographic data should have the open porosity space to characterise as foreground.Unusual features: Can be used together with the solution for the fluid flow for obtaining a combined topological-hydrodynamical characterisation.Additional comments: Our implementation was oriented for easy understanding, not computational speed. However, see section regarding memory implementation details, RAM-disk swapping strategy and parallelisation for details.Running time: Typical running time: 2 hours. Largest tested problem (10¹⁰ bytes): 1 day.     

Algorithms minimizing mean flow time: schedule-length properties

Summary The mean flow time of a schedule provides a measure of the average time that a task spends within a computer system, and also the average number of unfinished tasks in the system. The mean flow time of a schedule is defined to be the sum of the finishing times of all tasks in the system. On a system of identical processors O(nlog n) algorithms exist for determining minimal mean flow time schedules for n independent tasks. In general, there will be a large class C of schedules, of widely differing lengths, that all minimize mean flow time. The problem of finding the shortest schedule in C is NP-complete. We give heuristics that find schedules in C that are no more than 25% longer than the shortest schedule in C. The advantage of a short schedule is that processor utilization is high.Partial support provided by NSF Grant GJ-28290