Solution of incompressible fluid flow problems with heat transfer by means of an efficient RBF-FD meshless approach

The localized radial basis function collocation meshless method (LRBFCMM), also known as radial basis function generated finite differences (RBF-FD) meshless method, is employed to solve time-dependent, 2D incompressible fluid flow problems with heat transfer using multiquadric RBFs. A projection approach is employed to decouple the continuity and momentum equations for which a fully implicit scheme is adopted for the time integration. The node distributions are characterized by non-cartesian node arrangements and large sizes, i.e., in the order of $10^5$ nodes, while nodal refinement is employed where large gradients are expected, i.e., near the walls. Particular attention is given to the accurate and efficient solution of unsteady flows at high Reynolds or Rayleigh numbers, in order to assess the capability of this specific meshless approach to deal with practical problems. Three benchmark test cases are considered: a lid-driven cavity, a differentially heated cavity and a flow past a circular cylinder between parallel walls. The obtained numerical results compare very favourably with literature references for each of the considered cases. It is concluded that the presented numerical approach can be employed for the efficient simulation of fluid-flow problems of engineering relevance over complex-shaped domains

A numerical study of steady viscous flow past a circular cylinder

Numerical solutions have been obtained for steady viscous flow past a circular cylinder at Reynolds numbers up to 300. A new technique is proposed for the boundary condition at large distances and an iteration scheme has been developed, based on Newton's method, which circumvents the numerical difficulties previously encountered around and beyond a Reynolds number of 100. Some new trends are observed in the solution shortly before a Reynolds number of 300. As vorticity starts to recirculate back from the end of the wake region, this region becomes wider and shorter. Other flow quantities like position of separation point, drag, pressure and vorticity distributions on the body surface appear to be quite unaffected by this reversal of trends

Computational modelling of vortex shedding flows

This study describes the development and application of a two--<:limensional CFD method for vortex shedding flows past square and circular cylinders. The overall approach can be regarded as a compromise between the accuracy and computational costs, especially for high-Reynolds number flows. The latter are modelled by variants of the k - E eddy-viscosity model which is used in conjunction with wall functions. The governing equations, expressed through Cartesian vector and tensor components, are discretised using the finite volume method with a colocated storage arrangement for all variables. Body-fitted (non-orthogonal) structured or block-structured numerical grids can be used. Fully implicit, first-order accurate time discretisation is adopted, while the space discretisation is formally second-order accurate. In order to ensure a bounded solution, the high-resolution MINMOD and SMART schemes are implemented. The numerical method is validated against experimental data for various laminar flow situations: (i) single square and circular cylinders in a uniform flow, (ii) two circular cylinders in tandem submerged in a uniform flow and (iii) a circular cylinder in oscillatory flows. In the case of the uniform flow over single cylinders, the issues affecting the accuracy and reliability of two dimensional numerical solutions are addressed. It is shown that numerical uncertainties caused by a choice of the solution domain width (the blockage) very often cancel time and space discretisation errors. Further, advantages of high-resolution bounded schemes such as the MINMOD and SMART are confirmed. Variations of the mean drag coefficient and Strouhal number with Reynolds number are accurately predicted for the Reynolds number below 200, i.e. for two dimensional flow conditions. For these conditions, some physical features of vortex shedding are emphasized. For other flow configurations, parametric studies are conducted to investigate effects of additional factors on the integral vortex shedding parameters and flow regimes. In all cases, the present results compare well to the published experimental and numerical data. Various versions of the k - E model are considered for turbulent flow predictions. A new model, with an unsteady modification related to the production of the dissipation rate, is proposed. This model and the RNGmodel are validated against data for vortex shedding f{'om single square and circular cylinders. In the case of a square cylinder (Re = 20,000), both models yield satisfactory results for the integral parameters and most of the time-averaged and phase-averaged flow variables. These results stand comparison with those obtained by other models or LES methods. For a circular cylinder, the boundary layers are laminar before flow separation over a wide range of Reynolds numbers, up to 1 X 106 . On the other hand, the tested k - E models are based on the principal assumption that the flow is turbulent everywhere. Consequently, the flow separation is predicted wrongly which leads to unsccessful predictions of other vortex shedding results. Better results are obtained for the postcritical regime (Re > 106), where the boundary layers are turbulent before separation

Computation of Steady Incompressible Flows in Unbounded Domains

In this study we revisit the problem of computing steady Navier-Stokes flows in two-dimensional unbounded domains. Precise quantitative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical fluid dynamics. Following a review of key mathematical properties of such solutions related to the slow decay of the velocity field at large distances from the obstacle, we develop and carefully validate a spectrally-accurate computational approach which ensures the correct behavior of the solution at infinity. In the proposed method the numerical solution is defined on the entire unbounded domain without the need to truncate this domain to a finite box with some artificial boundary conditions prescribed at its boundaries. Since our approach relies on the streamfunction-vorticity formulation, the main complication is the presence of a discontinuity in the streamfunction field at infinity which is related to the slow decay of this field. We demonstrate how this difficulty can be overcome by reformulating the problem using a suitable background "skeleton" field expressed in terms of the corresponding Oseen flow combined with spectral filtering. The method is thoroughly validated for Reynolds numbers spanning two orders of magnitude with the results comparing favourably against known theoretical predictions and the data available in the literature.Comment: 39 pages, 12 figures, accepted for publication in "Computers and Fluids

Rough clustering for web transactions

Grouping web transactions into clusters is important in order to obtain better understanding of user's behavior. Currently, the rough approximation-based clustering technique has been used to group web transactions into clusters. It is based on the similarity of upper approximations of transactions by given threshold. However, the processing time is still an issue due to the high complexity for finding the similarity of upper approximations of a transaction which used to merge between two or more clusters. In this study, an alternative technique for grouping web transactions using rough set theory is proposed. It is based on the two similarity classes which is nonvoid intersection. The technique is implemented in MATLAB ® version 7.6.0.324 (R2008a). The two UCI benchmark datasets taken from: http:/kdd.ics.uci.edu/ databases/msnbc/msnbc.html and http:/kdd.ics.uci.edu/databases/ Microsoft / microsoft.html are opted in the simulation processes. The simulation reveals that the proposed technique significantly requires lower response time up to 62.69 % and 66.82 % as compared to the rough approximation-based clustering, severally. Meanwhile, for cluster purity it performs better until 2.5 % and 14.47%, respectively