CABARET scheme in vorticity-velocity variables for the numerical modeling of ideal fluid motion in a two-dimensional domain

A modification of the CABARET scheme is proposed for the numerical solution of equations of ideal fluid motion in vorticity-velocity variables. The dissipative and dispersive properties of the obtained numerical algorithm were investigated for the problem of an isolated vortex. Calculations were performed for decaying homogeneous isotropic turbulence on grids of varying density. In all investigated grids, the spectral density of the kinetic energy was found to obey the ??-3?? law, which conforms to the Kraichnan-Batchelor theory. The structural functions of the obtained vortex flow conform to the law derived using the dimension theory.     

Topological shape optimization of geometrically nonlinear structures using level set method

Using the level set method, a topological shape optimization method is developed for geometrically nonlinear structures in total Lagrangian formulation. The structural boundaries are implicitly represented by the level set function, obtainable from “Hamilton-Jacobi type” equation with “up-wind scheme,” embedded into a fixed initial domain. The method minimizes the compliance through the variations of implicit boundary, satisfying an allowable volume requirement. The required velocity field to solve the Hamilton-Jacobi equation is determined by the descent direction of Lagrangian derived from an optimality condition. Since the homogeneous material property and implicit boundary are utilized, the convergence difficulty is significantly relieved.     

A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk

In this paper, the problem of optimal feedrate planning along a curved tool path for 3-axis CNC machines with the acceleration and jerk limits for each axis and the tangential velocity bound is addressed. It is proved that the optimal feedrate planning must be “Bang–Bang” or “Bang–Bang-Singular” control, that is, at least one of the axes reaches its acceleration or jerk bound, or the tangential velocity reaches its bound throughout the motion. As a consequence, the optimal parametric velocity can be expressed as a piecewise analytic function of the curve parameter u. The explicit formula for the velocity function when a jerk reaches its bound is given by solving a second-order differential equation. Under a “greedy rule”, an algorithm for optimal jerk confined feedrate planning is presented. Experiment results show that the new algorithm can be used to reduce the machining vibration and improve the machining quality.     

Analysis of a variational multiscale method for Large–Eddy simulation and its application to homogeneous isotropic turbulence

In this paper a variational multiscale method based on local projection and grad–div stabilization for Large–Eddy simulation for the incompressible Navier–Stokes problem is considered. An a priori error estimate is given for a case with rather general nonlinear (piecewise constant) coefficients of the subgrid models for the unresolved scales of velocity and pressure. Then the design of the subgrid scale models is specified for the case of homogeneous isotropic turbulence and studied for the standard benchmark problem of decaying homogeneous isotropic turbulence.     

Absolute stability of third-order systems: A numerical algorithm

The problem of absolute stability is one of the oldest open problems in the theory of control. Even for the particular case of second-order systems a complete solution was presented only very recently. For third-order systems, the most general theoretical results were obtained by Barabanov. He derived an implicit characterization of the “most destabilizing” nonlinearity using a variational approach. In this paper, we show that his approach yields a simple and efficient numerical scheme for solving the problem in the case of third-order systems. This allows the determination of the critical value where stability is lost in a tractable and accurate fashion. This value is important in many practical applications and we believe that it can also be used to develop a deeper theoretical understanding of this interesting problem.     

Impact of the large cross-modulation parameter on the collision dynamics of quasi-particles governed by vector NLSE

For the Coupled Nonlinear Schrödinger Equations (CNLSE) we construct a conservative fully implicit scheme (in the vein of the scheme with internal iterations proposed in [C.I. Christov, S. Dost, G.A. Maugin, Inelasticity of soliton collisions in system of coupled nls equations, Physica Scripta 50 (1994) 449–454.]). Our scheme makes use of complex arithmetic which allows us to reduce the computational time fourfold. The scheme conserves the “mass”, momentum, and energy.     

Discrete logarithm based chameleon hashing and signatures without key exposure

Chameleon signatures simultaneously provide the properties of non-repudiation and non-transferability for the signed message. However, the initial constructions of chameleon signatures suffer from the key exposure problem of chameleon hashing. This creates a strong disincentive for the recipient to compute hash collisions, partially undermining the concept of non-transferability. Recently, some constructions of discrete logarithm based chameleon hashing and signatures without key exposure are presented, while in the setting of gap Diffie–Hellman groups with pairings.In this paper, we propose the first key-exposure free chameleon hash and signature scheme based on discrete logarithm systems, without using the gap Diffie–Hellman groups. This provides more flexible constructions of efficient key-exposure free chameleon hash and signature schemes. Moreover, one distinguishing advantage of the resulting chameleon signature scheme is that the property of “message hiding” or “message recovery” can be achieved freely by the signer, i.e., the signer can efficiently prove which message was the original one if he desires.     

ODTLES: A multi-scale model for 3D turbulent flow based on one-dimensional turbulence modeling

A novel multi-scale approach for extending the one-dimensional turbulence (ODT) model of [A.R. Kerstein. One-dimensional turbulence: model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows, J. Fluid Mech. 392 (1999) 277] to treat turbulent flow in three-dimensional (3D) domains is described. In this model, here called ODTLES, 3D aspects of the flow are captured by embedding three, mutually orthogonal, one-dimensional ODT domain arrays within a coarser 3D mesh. The ODTLES model is obtained by developing a consistent approach for dynamically coupling the different ODT line sets to each other and to the large scale processes that are resolved on the 3D mesh. The model is implemented computationally and its performance is tested by performing simulations of decaying isotropic turbulence at two different Reynolds numbers and comparing to the experimental data of [H. Kang, S. Chester, C. Meneveau. Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulations, J. Fluid Mech. 480 (2003) 129; G. Comte-Bellot, S. Corrsin, Simple Eulerian correlation of full-and narrow band velocity signals in grid-generated ’isotropic’ turbulence, J. Fluid Mech. 48 (1971) 273].     

Critical thermodynamic evaluation and optimization of the MnO–“ TiO2 ”–“ Ti2O3 ” system

A complete review, critical evaluation, and thermodynamic optimization of the phase equilibrium and thermodynamic properties of the MnO–“ TiO₂”–“ Ti₂O₃” systems at 1 bar pressure are presented. The molten oxide phase was described by the Modified Quasichemical Model. The Gibbs energy of spinel, pyrophanite and pseudobrookite solid solutions were modeled using the Compound Energy Formalism, and rutile solid solution was treated as a simple Henrian solution. Manganosite solid solution was assumed to dissolve both Ti⁴⁺ and Ti³⁺. A set of optimized model parameters for all phases was obtained which reproduces all available reliable thermodynamic and phase equilibrium data within experimental error limits from 25 ^°C to above the liquidus temperatures over the entire composition ranges and in the range of pO₂ from 10⁻²⁰ to 10⁻⁷ bar. Complex phase relationships in these systems have been elucidated, and discrepancies among the data have been resolved. The database of model parameters can be used along with software for Gibbs energy minimization in order to calculate any phase diagram section or thermodynamic properties.     

Analysis of the energy budget in turbulent channel flow using orthogonal wavelets

The spatial and scale statistics of turbulence kinetic energy are examined in turbulent channel flow at Re_τ = 300 using the orthonormal wavelet transform. The behaviour of the production, viscous and transfer terms is examined in terms of their variation with both space and scale. All terms are numerically large at wavenumbers at which a −5/3 slope is apparent in the velocity spectra, and they all exhibit significant spatial variability as evidenced by large flatnesses which increase with decreasing scale size. The flatness of terms involving transfer are particularly large. Attention focusses primarily on the sublayer and local-equilibrium regions: in the former, scale-to-scale flux is large and negative and consistent with conventional “backscatter” in Fourier space. In the linear sublayer, the flux is positive, consistent with Couette-like vortex stretching. The present work paves the way for close scrutiny of those components of the subgrid-scale stress that contribute most to the subgrid energy flux in large-eddy simulation of near-wall turbulent flows.     

Bubble interactions for the Mullins–Sekerka problem: Some case examples

The Mullins–Sekerka free boundary problem originates from the study of solidification and liquidation of materials where material is transported by diffusion. In the present paper we explore dynamics of bubbles for the Mullins–Sekerka problem. Using a set of ordinary differential equations for the radii and the centers, we numerically simulate the relevant interactions in both “two-dimensional” and “three-dimensional” settings. Our results illustrate how larger bubbles grow at the expense of smaller ones and highlight the role of additional factors such as the initial inter-bubble distance or weak asymmetries in the bubble position in the ensuing dynamics. One novel feature in comparison with earlier works is the possibility to continue for the three-dimensional case the simulation past the points where one of the bubbles disappears.     

A conservative model for unsteady flows in deformable closed pipes and its implicit second-order finite volume discretisation

We present a one-dimensional model for compressible flows in a deformable pipe which is an alternative to the Allievi equations and is intended to be coupled in a “natural way” with the shallow water equations to simulate mixed flows. The numerical simulation is performed using a second-order linearly implicit scheme adapted from the Roe scheme. The validation is performed in the case of water hammer in a rigid pipe: we compare the numerical results provided by an industrial code with those of our spatial second-order implicit scheme. It appears that the maximum value of the pressure within the pipe for large CFL numbers and a coarse discretisation is accurately computed.     

Pseudo-spectral numerical simulation of miscible fluids with a high density ratio

A computational algorithm is described for direct numerical simulation (DNS) of turbulent mixing of two incompressible miscible fluids having greatly differing densities. The algorithm uses Fourier pseudo-spectral methods to compute spatial derivatives and a fractional step method involving the third-order Adams-Bashforth-Moulton predictor-corrector scheme to advance the solution in time. The pressure projection technique is shown to eliminate stability problems, previously observed, when the ratio of the densities in the two streams is as high as 35. The algorithm is investigated in detail for mixing in isotropic homogeneous turbulence of two fluids with a density ratio of 10. The limit on the density ratio is imposed so that the flow is both everywhere turbulent and spatially resolved. Both fluids have the same molecular viscosities, the nominal Schmidt number is 0.7, and the initial nominal Reynolds number based on the integral length scale and the rms velocity is 158. No body force is considered. It is shown that the pressure projection scheme does not limit the temporal accuracy of the solution when periodic boundary conditions are used, but that it significantly affects the stability of the simulations. It is also shown that the rate at which turbulence kinetic energy dissipates averaged for the whole computational domain is almost unaffected by density ratio.     

VRML animated model watermarking scheme using geometry and interpolator nodes

Distinct from image and video watermarking, a watermarking scheme for 3D animation content is required in the 3D industry market for various applications. This paper develops a watermarking scheme for copyright protection and authentication of 3D animation content. A 3D animated model generally has a hierarchical structure with a number of transform nodes of a geometry node and an interpolator node for the timeline in contrast to a 3D polygon mesh model. The proposed scheme embeds not only a robust watermark into the geometry node for copyright protection but also a fragile watermark into the position and orientation interpolators for content authentication. We named the former “robust geometry watermarking” and the latter “fragile interpolator watermarking”. The proposed scheme performs the two watermarking schemes independently to realize simultaneously robust and fragile watermarked 3D animated model. Experimental results confirm that a watermark embedded by geometry watermarking robust to many attacks from commercial 3D editing tools while a watermark embedded by interpolator watermarking fragile to the same attacks.     

Cabaret scheme for two-dimensional incompressible fluid in terms of the stream function-vorticity variables

In the present work, the Cabaret method is generalized to the case of two-dimensional incompressible fluid in terms of the stream function-vorticity variables. Using the example of the solitary vortex problem, the high quality of the obtained algorithm in terms of its dissipative and dispersion properties is demonstrated. In the problem about decaying homogeneous isotropic turbulence, the slopes of the energy spectra for all grids (16 × 16, 32 × 32, 64 × 64, 128 × 128) are (−3) up to the highest harmonics, which coincides with Batchelor’s theory.     

Broadband slat noise prediction based on CAA and stochastic sound sources from a fast random particle-mesh (RPM) method

The application of a low-cost computational aeroacoustics (CAA) approach to a slat noise problem is studied. A fast and efficient stochastic method is introduced to model the unsteady turbulent sound sources in the slat-cove of a high-lift airfoil. It is based on the spatial convolution of spatiotemporal white-noise and can reproduce target distributions of turbulence kinetic energy and length scales, such as that provided by a RANS computation of the time-averaged turbulent flow problem. The computational method yields a perfectly solenoidal velocity field. For homogeneous isotropic turbulence, the complete second-order two-point velocity correlation tensor is realized exactly. Two RANS turbulence models are applied to the slat noise problem to study how sensitive the aeroacoustics predictions depend on turbulence kinetic energy predictions. Results for the sound generation at the slat are given for a Menter SST turbulence model with and without Kato-Launder modification. The aeroacoustic simulations yield a characteristic narrow band spectrum that compares very well with the experimental data. The directivities found point toward an edge noise mechanism at the slat as the main cause for slat noise sound generation.     

Coherent structure formation,phase correlations,and finite-size effects in 2D turbulence

General conditions for the formation of long-lived coherent vortices in decaying and force-driven 2-D turbulence are investigated. It is shown by a series of numerical simulations that the emergence of closed streamlines leading to the trapped trajectories of vorticity is a necessary, but not sufficient condition for this phenomenon, so that these trapped trajectories may be considered only as seed vortices. Numerical experiments which demonstrate the relations between phase correlations, finite-size effects, and the formation of coherent vortices in 2-D decaying turbulence are presented. It is shown that there is a universal dimensionless time for the onset of intermittency in the flow which corresponds to the time of establishment of phase correlations. The stricter conditions for appearance of coherent vortices in forced turbulence in comparison with decaying turbulence are associated with phase mixing introduced by random forcing. The universal features of decaying turbulence are discussed in terms of phase portraits based on inviscid constants of motion and their decay rates.     

Flow pattern around an appended tanker hull form in simple maneuvering conditions

A detailed computational study is presented of the flow pattern around the Esso Osaka with rudder in simple maneuvering conditions: “static rudder” and “pure drift”. The objectives are: (1) apply RANS for maneuvering simulation; (2) perform verification and validation on field quantities; (3) characterize flow pattern; and (4) correlate behavior of the integral quantities with the flow field. The general-purpose code CFDSHIP-IOWA is used. The free surface is neglected and the two-equation k-ω turbulence model is used. The levels of verification of the velocity components for the “straight-ahead”, “static rudder” and “pure drift” conditions show ranges from 5.5% to 28.3% of free stream, U₀, for the axial velocity U and 2.5-29.1%U₀ for the cross flow (V, W). Qualitative validation against limited experimental data shows encouraging results with respect to trends and levels. The flow pattern is characterized by fore and aft body bilge and side vortices, which are similar for “straight-ahead” and “static rudder” conditions, except in close vicinity of the rudder. The “pure drift” condition shows strong asymmetry on windward vs. leeward sides and a more complex vortex system with additional bilge vortices. Similarities and differences with data for other tanker, container, and surface combatant hulls and relation between flow pattern and forces and moments are discussed. Future work focuses on influence of propeller.     

On the exploitation of CDF based wireless scheduling

Channel-aware scheduling strategies – such as the CDF scheduler (CS) algorithm – provide an effective mechanism for utilizing the channel data rate for improving throughput performance in wireless data networks by exploiting channel fluctuations. A highly desired property of such a scheduling strategy is that its algorithm is stable, in the sense that no user has incentive “cheating” the algorithm in order to increase his/hers channel share (on the account of others). Considering a single user we show that no such user can increase his/hers channel share by misreporting the channel capacity. In contrast, considering a group of users, we present a scheme by which coordination allows them to gain permanent increase in both their time slots share and in their throughput at the expense of others, by misreporting their rates. We show that for large populations consisting of regular and coordinated users in equal numbers, the ratio of allocated time slots between a coordinated and a regular user converges to e − 1 ≈ 1.7. Our scheme targets the very fundamental principle of CS (as opposed to just attacking implementation aspects), which bases its scheduling decisions on the Cumulative Distribution Function (CDF) of the channel rates reported by users. Our scheme works both for the continuous channel spectrum and the discrete channel spectrum versions of the problem. Finally, we outline a modified CDF scheduler immune to such attacks.     

Erratum to “Minimum cost flows with minimum quantities” [Information Processing Letters 111 (11) (2011) 533–537]

This note identifies an error in the fully polynomial-time approximation scheme on series-parallel graphs presented in our paper “Minimum cost flows with minimum quantities” which appeared as [Sven O. Krumke, Clemens Thielen, Minimum cost flows with minimum quantities, Information Processing Letters 111 (11) (2011) 533–537]. In fact, we prove inapproximability of the problem on series-parallel graphs and of a related problem, thereby identifying a similar error in a related paper.