• Wind and Structures
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• v.5 no.2_3_4
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• pp.177-192
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• 2002

Computation solutions for the flow around a cube, which were generated as part of the Computational Wind Engineering 2000 Conference Competition, are compared with full-scale measurements. The three solutions shown all use the RANS approach to predict mean flow fields. The major differences appear to be related to the use of the standard $k-{\varepsilon}$, the MMK $k-{\varepsilon}$ and the RNG $k-{\varepsilon}$ turbulence models. The inlet conditions chosen by the three modellers illustrate one of the dilemmas faced in computational wind engineering. While all modeller matched the inlet velocity profile to the full-scale profile, only one of the modellers chose to match the full-scale turbulence data. This approach led to a boundary layer that was not in equilibrium. The approach taken by the other modeller was to specify lower inlet turbulent kinetic energy level, which are more consistent with the turbulence models chosen and lead to a homogeneous boundary layer. For the $0^{\circ}$ case, wind normal to one face of the cube, it is shown that the RNG solution is closest to the full-scale data. This result appears to be associated with the RNG solution showing the correct flow separation and reattachment on the roof. The other solutions show either excessive separation (MMK) or no separation at all (K-E). For the $45^{\circ}$ case the three solutions are fairly similar. None of them correctly predicting the high suctions along the windward edges of the roof. In general the velocity components are more accurately predicted than the pressures. However in all cases the turbulence levels are poorly matched, with all of the solutions failing to match the high turbulence levels measured around the edges of separated flows. Although all of the computational solutions have deficiencies, the variability of results is shown to be similar to that which has been obtained with a similar comparative wind tunnel study. This suggests that the computational solutions are only slightly less reliable than the wind tunnel.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.137-162
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• 2024

This paper consists of two significant aims. The first aim of this paper is to establish the criteria for the existence of solutions to nonlinear Volterra-Fredholm (V-F) fractional integral equations on [0, L], where 0 < L < ∞. The fractional integral is described here in the sense of the Katugampola fractional integral of order λ > 0 and with the parameter β > 0. The concepts of the fixed point theorem and the measure of noncompactness are used as the main tools to prove the existence of solutions. The second aim of this paper is to introduce a computational method to obtain approximate numerical solutions to the considered problem. This method is based on the Fibonacci wavelets with collocation technique. Besides, the results of the error analysis and discussions of the accuracy of the solutions are also presented. To the best knowledge of the authors, this is the first computational method for this generalized problem to obtain approximate solutions. Finally, two examples are discussed with the computational tables and convergence graphs to interpret the efficiency and applicability of the presented method.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.39-47
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• 2003

Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7］are generalized and improved.

• Computational Structural Engineering : An International Journal
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• v.1 no.1
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• pp.49-57
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• 2001

This paper presents exact solutions for the modal stress-resultant distributions for vibrating rectangular Mindlin plates involving two opposite sides simply supported while the other two sides free. These exact stress-resultants of vibrating plates with free edges, hitherto unavailable, are very important because they serve as benchmark solutions for checking numerical solutions and methods. Using the exact solutions of a square plate, this paper highlights the problem of determining accurate stress-resultants, especially the transverse shear forces and twisting moments in thin plates, when employing the widely used numerical methods such as the Ritz method and the finite element method. Thus, this study shows that there is a need for researchers to develop refinements to the Ritz method and the finite element method for determining very accurate stress-resultants in vibrating plates with free edges.

• Journal of computational fluids engineering
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• v.21 no.3
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• pp.64-70
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• 2016

Multiple solutions in natural convection of water with Pr=7 between two horizontal plates with small magnitude non-uniform temperature distribution in the upper plate is numerically investigated. The dimensionless temperature of upper plate is ${\theta}={\epsilon}sinkx$. Two upright cells are formed over one wave length in the conduction-dominated regime of small Rayleigh number. However, multicellular convection occurs above a critical Rayleigh number for small wave number. When k = 1.5, dual solutions are found and a transition of $6{\rightarrow}4$ eddy flow occurs with decrease of Rayleigh number. When k = 0.75, two, three, four and five multiple solutions are observed. Transitions of $14{\rightarrow}12$, $12{\rightarrow}10$, $10{\rightarrow}8$ and $6{\rightarrow}8$ eddy flow occur with decrease of Rayleigh number.

• Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.295-311
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• 2016

This paper addresses to the flowshop scheduling problem with blocking constraints. The objective is to minimize the makespan criterion. We propose a hybrid combinatorial particle swarm optimization algorithm (HCPSO) as a resolution technique for solving this problem. At the initialization, different priority rules are exploited. Experimental study and statistical analysis were performed to select the most adapted one for this problem. Then, the swarm behavior is tested for solving a combinatorial optimization problem such as a sequencing problem under constraints. Finally, an iterated local search algorithm based on probabilistic perturbation is sequentially introduced to the particle swarm optimization algorithm for improving the quality of solution. The computational results show that our approach is able to improve several best known solutions of the literature. In fact, 76 solutions among 120 were improved. Moreover, HCPSO outperforms the compared methods in terms of quality of solutions in short time requirements. Also, the performance of the proposed approach is evaluated according to a real-world industrial problem.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.110-117
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• 2004

The aim of a benchmark study is carried out nine methods are employed for ULS analysis which implicitly predict the ultimate strength of aluminium stiffened panels under axial compression. For this purpose, DNV PULS, experimental and numerical data on the ultimate strength of panels were collected. Comparison of these experimental / numerical, DNV PULS / numerical, results with theoretical solutions by the candidate methods is performed. Also it's compared that ALPS/ULSAP program is based on closed-form formula for the ULS of plates and grillages under axial compression. It is considered that ALPS/ULSAP methodology provides quite accurate and reasonable ULS calculations by a comparison with more refined FEA. Comparison of these experimental data, numerical, computational software results with the simplified solutions obtained by the candidate methods is then performed. The model uncertainties associated with the candidate methods are studied in terms of mean bias and COV (i.e., coefficient of variation) against experiments and numerical solutions, and the relative performance of the various methods is discussed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.3-10
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• 2003

The use of frequency-dependent dynamic stiffness matrix (or spectral element matrix) in structural dynamics may provide very accurate solutions, while it reduces the number of degrees-of-freedom to improve the computational efficiency and cost problems. Thus, this paper develops a spectral element model for the thin plates moving with constant speed under uniform in-plane tension and gravity. The concept of Kantorovich method and the principle of virtual displacement is used in the frequency-domain to formulate the dynamic stiffness matrix. The present spectral element model is evaluated by comparing its solutions with the exact analytical solutions. The effects of moving speed, in-plane tension and gravity on the natural frequencies of the plate are numerically investigated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.192-199
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• 2002

The use of frequency-dependent dynamic stiffness matrix (or spectral element matrix) in structural dynamics may provide very accurate solutions, while it reduces the number of degrees-of-freedom to improve the computational efficiency and cost problems. Thus, this paper develops a spectral element model for the thin plates moving with constant speed under uniform in-plane tension. The concept of Kantorovich method is used in the frequency-domain to formulate the dynamic stiffness matrix. The present spectral element model is evaluated by comparing its solutions with the exact analytical solutions. The effects of moving speed and in-plane tension on the flexural wave dispersion characteristics and natural frequencies of the plate are numerically investigated.

• Journal of computational fluids engineering
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• v.21 no.1
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• pp.10-18
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• 2016

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.