Abstract

A numerical study was conducted using the finite difference technique to examine the mechanism of energy transfer as well as turbulence in the case of turbulent flow fully developed in the channel with substantially constant wall temperature and constant heat flow conditions. The methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties by placing itself in the equilibrium hypothesis of an axisymmetric. The global equations and the initial and boundary conditions acting on the problem are configured in dimensionless form in order to predict the characteristics of the turbulent fluid flow inside the tube. Thus, using Thomas' algorithm, a program in FORTRAN version 95 was developed to numerically solve the discretized form of the system of equations describing the problem. Finally, using this elaborate program, we were able to simulate the flow characteristics, changing some parameters involved such as Reynolds number, the Prandtl number and the Peclet number, along the longitudinal coordinate to obtain important results of the thermal model. These are discussed in detail in this work. Comparisons between literatures correlation data and the calculated simulation indicate that the results are a good match to previously published quantities.

Abstract

Abstract

This article proposes a parallel implementation using a multicore environment with MPI to the solution of the linear system resulting from the discretization of the Poisson equation in 2D using finite differences and the iterative method of Jacobi. The size of the domain and its corresponding discretization result in a system of linear equations where the number of variables can be millions. The magnitude of the problem allows the algorithm to be highly scalable in parallel; this means that by increasing the number of processors available to solve the system, the execution time will improve considerably. However, as the number of processors increases, the communication work also increases, which stops its performance. Therefore, this article proposes re-engineering the parallel algorithm focused on memory management to speed up its execution and improve its effectiveness.

Abstract

Abstract

The pseudopotential method has grown as a powerful tool for multiphase fluid flow simulations within the lattice Boltzmann method framework. We consider that due to its simplicity and computational efficiency, the pseudopotential method could be explored also inside the framework of more traditional Computational Fluid Dynamic methods such as Finite Difference, Finite Volume or Finite Element methods. Following this idea, in this work we start from the macroscopic equations resulting from the pseudopotential lattice Boltzmann method and discretize it by a simple Finite Difference scheme. This pseudopotential based finite difference method is then tested in different benchmark problems such as a planar interface, a smooth droplet oscillation, and a single droplet evaporation. Excellent results were obtained in all tests. One of the advantages of the proposed method is that mesh refinement is straightforward, and converged solutions can be used as a tool of validation for the lattice Boltzmann method. Results indicate that the pseudopotential method is suitable to be used with standard discretization methods such as Finite Difference and that in future works more robust discretizations can be used to further enhance the pseudopotential method application.

Abstract

Abstract

In order to reduce the discretization error, in this paper, Richardson’s Extrapolation and Convergence Error Estimator were used to investigating the buckling problem convergence. The main objective was to verify the convergence order of the stepped column problem and to define a consistent moment of inertia at the point of variation of the cross-section. The variable of interest was the critical buckling load obtained by the Finite Difference Method. The convergent solution obtained errors less than 10^^-8, and this work showed that the best solution is not defined by excessive mesh refinement, but by the solution convergence analysis.

Abstract

This work aims to evaluate a parallelizable approximate solution model for the wave equation. For that, we used the temporal sweep known as the Waveform Relaxation method to guarantee the parallelization in space. However, this technique has limitations for this class of problems. Therefore, we proposed the combination of the Subdomain method in a non-conventional way in time with the Multigrid method, intending to reduce computational time and improve the convergence factors. In this work, we presented the mathematical analysis of the stability of the discretization model, which uses the Central Finite Difference method with weighting at each time step. As an application of the proposed method, in addition to a problem with a known analytical solution, we solved a wave propagation problem with reflection and phase inversion.

Abstract

It is difficult to detect small foreign objects such as hair and soft plastics in dry foods. In our laboratory, an electrostatic separator of small foreign objects in dry foods was developed. The separator consists of a grounded inclined rotating drum, a cylindrical electrode fixed at the centre of the drum, and a suction device. The principle of the separation is based on the difference in the charge per unit mass of the dry food and foreign objects. Although it was found that it is possible to obtain a high purity and a high recovery rate of foods using this separator, the understanding of the separation mechanism is still limited. In this study, we numerically investigated the separation behaviours of foreign objects and dry foods in the inclined rotating drum. The behaviours of the foreign objects and dry foods were calculated, considering the electrostatic force. The electric field strength was calculated by the finite difference method. The effect of the inclination angle of the rotating drum on the trajectory of the particles to be separated was investigated. To examine the validity of the calculation method, the experimental result was compared with the calculated result.

Abstract

In this work, full stress tensor components regarding stress state for a simmetrical composite laminate under uniform uniaxial extension have been determined. Off-plane stresses are specially meaningful due to the fact that they are responsible for failure mechanisms such as delamination and shear stress cracking. A finite difference scheme has been used to solve internal equilibrium equations subjected to stress-free boundary conditions along boundary lines; moreover symmetry considerations have been made. In such way, we get an improvement in solutions in contrast with results obtained following bidimensional reasoning and using laminate based elements. Off-plane stresses for differents ply-sequences have been evaluated and maximum and minimum values for different fibers orientations were explored.