Simulated annealing and genetic algorithms for minimizing mean flow time in an open shop

This paper considers the problem of scheduling n jobs on m machines in an open shop environment so that the sum of completion times or mean flow time becomes minimal. It continues recent work by Bräsel et al. [H. Bräsel, A. Herms, M. Mörig, T. Tautenhahn, T. Tusch, F. Werner, Heuristic constructive algorithms for open shop scheduling to minmize mean flow time, European J. Oper. Res., in press (doi.10.1016/j.ejor.2007.02.057)] on constructive algorithms. For this strongly NP-hard problem, we present two iterative algorithms, namely a simulated annealing and a genetic algorithm. For the simulated annealing algorithm, several neighborhoods are suggested and tested together with the control parameters of the algorithm. For the genetic algorithm, new genetic operators are suggested based on the representation of a solution by the rank matrix describing the job and machine orders. Extensive computational results are presented for problems with up to 50 jobs and 50 machines, respectively. The algorithms are compared relative to each other, and the quality of the results is also estimated partially by a lower bound for the corresponding preemptive open shop problem. For most of the problems, the genetic algorithm is superior when fixing the same number of 30 000 generated solutions for each algorithm. However, in contrast to makespan minimization problems, where the focus is on problems with an equal number of jobs and machines, it turns out that problems with a larger number of jobs than machines are the hardest problems.     

Numerical investigation of the effects of sluice spillway roof profiles on the hydraulic characteristics

There is a need for evolving hydraulically efficient roof profile of bellmouth for high head sluice spillways, as sluice roof is susceptible to cavitation damage. In this paper, formulation and development of a numerical model for simulating the spillway flow and its application to a sluice spillway are presented. The main focus of the simulation study is to apply the developed model to investigate the effects of sluice roof profile geometry on the pressure distribution, the discharge coefficient and the nature of flow regime within the sluice bellmouth. From the analysis of results for eight different roof profiles by varying the entry and exit angles of elliptic bellmouth transition, some important observations have been suggested, which are of practical relevance to hydraulic design engineers. The numerical model results are compared for one profile with physical model study. The simulated results are in close agreement with the measured values. Copyright © 2007 John Wiley & Sons, Ltd.     

A conservative unstructured scheme for rapidly varied flows

This article introduces a new semi‐implicit, staggered finite volume scheme on unstructured meshes for the modelling of rapidly varied shallow water flows. Rapidly varied flows occur in the inundation of dry land during flooding situations. They typically involve bores and hydraulic jumps after obstacles such as road banks. Near such sudden flow transitions, the grid resolution is often low compared with the gradients of the bathymetry. Locally the hydrostatic pressure assumption may become invalid. In these situations, it is crucial to apply the correct conservation properties to obtain accurate results. An important feature of this scheme is therefore its ability to conserve momentum locally or, by choice, preserve constant energy head along a streamline. This is achieved using a special interpolation method and control volumes for momentum. The efficiency of inundation calculations with locally very high velocities, and in the case of unstructured meshes locally very small grid distances, is severely hampered by the Courant condition. This article provides a solution in the form of a locally implicit time integration for the advective terms that allows for an explicit calculation in most of the domain, while maintaining unconditional stability by implicit calculations only where necessary. The complex geometry of flooded urban areas asks for the flexibility of unstructured meshes. The efficient calculation of the pressure gradient in this, and other semi‐implicit staggered schemes, requires, however, an orthogonality condition to be put on the grid. In this article a simple method is introduced to generate unstructured hybrid meshes that fulfil this requirement. Copyright © 2008 John Wiley & Sons, Ltd.     

Conceptual linearization of Euler governing equations to solve high speed compressible flow using a pressure‐based method

The main objective of the current work is to introduce a new conceptual linearization strategy to improve the performance of a primitive shock‐capturing pressure‐based finite‐volume method. To avoid a spurious oscillatory solution in the chosen collocated grids, both the primitive and extended methods utilize two convecting and convected momentum expressions at each cell face. The expressions are obtained via a physical‐based discretization of two inclusive statements, which are constructed via a novel incorporation of the continuity and momentum governing equations. These two expressions in turn provide a strong coupling among the Euler conservative statements. Contrary to the primitive work, the linearization in the current work respects the definitions and essence of physics behind deriving the Euler governing equations. The accuracy and efficiency of the new formulation are then investigated by solving the shock tube as a problem with moving normal and expansion waves and the converging‐diverging nozzle as a problem with strong stationary normal shock. The results show that there is good improvement in performance of the primitive pressure‐based shock‐capturing method while its superior accuracy is not deteriorated at all. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Three-dimensional flow over a stretching surface in a viscoelastic fluid

This article looks at the hydrodynamic elastico-viscous fluid over a stretching surface. The equations governing the flow are reduced to ordinary differential equations, which are analytically solved by applying an efficient technique namely the homotopy analysis method (HAM). The solutions for the velocity components are computed. The numerical values of wall skin friction coefficients are also tabulated. The present HAM solution is compared with the known exact solution for the two-dimensional flow and an excellent agreement is found.     

A parallel computational method for simulating two‐phase gel dynamics on a staggered grid

We develop a parallel computational algorithm for simulating models of gel dynamics where the gel is described by two phases, a networked polymer and a fluid solvent. The models consist of transport equations for the two phases, two coupled momentum equations, and a volume‐averaged incompressibility constraint. Multigrid with Vanka‐type box‐relaxation scheme is used as preconditioner for the Krylov subspace solver (GMRES) to solve the momentum and incompressibility equations. Through numerical experiments of a model problem, the efficiency, robustness and scalability of the algorithm are illustrated. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonlinear resonance in viscous films on inclined wavy planes

We study nonlinear resonance in viscous gravity-driven films flowing over undulated substrates. Numerical solution of the full, steady Navier–Stokes equations is used to follow the emergence of the first few free-surface harmonics with increasing wall amplitude, and to study their parametric dependence on film thickness, inertia and capillarity. Bistable resonance is computed for steep enough bottom undulations. As an analytic approach, we apply the integral boundary-layer method and derive an asymptotic equation valid for rather thin films. The analysis recovers the key numerical findings and provides qualitative understanding. It shows that higher harmonics are generated by a nonlinear coupling of the wall with lower-order harmonics of the free surface. It also accounts for bistable resonance, and produces a minimum model whose solution is similar to that of the Duffing oscillator.     

Can shadowing mimic the QCD phase transition?

The directed flow of protons is studied in the quark-gluon string model as a function of the impact parameter for S+S and Pb+Pb reactions at 160 AGeV/c. A significant reduction of the directed flow in midrapidity range, which can lead to the development of the antiflow, is found due to the absorption of early emitted particles by massive spectators (shadowing effect). This effect can mimic the formation of the quark-gluon plasma (QGP). However, in the absorption scenario the antiflow is stronger for the system of light colliding nuclei than for the heavy ones, while in the case of the plasma creation the effect should be opposite.     

Coupled Amplitude-Streaming Flow Equations for Nearly Inviscid Faraday Waves in Small Aspect Ratio Containers

Summary. We derive a set of asymptotically exact coupled amplitude-streaming flow ({CASF}) equations governing the evolution of weakly nonlinear nearly inviscid multimode Faraday waves and the associated streaming flow in finite geometries. The streaming flow is found to play a particularly important role near mode interactions. Such interactions come about either through a suitable choice of parameters or through breaking of degeneracy among modes related by symmetry. An example of the first case is provided by the interaction of two nonaxisymmetric modes in a circular container with different azimuthal wavenumbers. The second case arises when the shape of the container is changed from square to slightly rectangular, or from circular to slightly noncircular but with a plane of symmetry. The generation of streaming flow in each of these cases is discussed in detail and the properties of the resulting CASF equations are described. A preliminary analysis suggests that these equations can resolve discrepancies between existing theory and experimental results in the first two of the above cases.     

A vortex axis and vortex core border grid adaptation algorithm

In the design process of hydrodynamical and aerodynamical technical applications, the numerical simulation of massively separated vortical flow is crucial for predicting, for example, lift or drag. To obtain reliable numerical results, it is mandatory to accurately predict the physical behavior of vortices. Thus, the dominant vortical flow structures have to be resolved in detail, which requires a local grid refinement and certain adaptation techniques. In this paper, a vortex flow structure adaptation algorithm is presented, which is particularly designed for local grid refinement at vortex axes positions and associated vortex core border locations. To this end, a fast and efficient vortex axis detection scheme is introduced and the algorithm for the vortex core border determination is explained. As the interaction between vortices makes the assignment of grid points to a certain vortex axis difficult, a helicity‐based vortex distinction approach in combination with a geometrical rotational sensor is developed. After describing the combined different techniques in detail, the vortex feature adaptation algorithm is applied to analytical and more realistic examples, which show that the described grid adaptation algorithm is able to enhance the grid cell resolution locally such that all significant vortical flow phenomena are resolved. Copyright © 2008 John Wiley & Sons, Ltd.