A finite difference scheme for inviscid flows with non-eequilibrium chemistry and internal energy

A finite difference scheme is presented for the inviscid terms of the equations of compressible fluid dynamics with general non-equilibrium chemistry and internal energy.

A finite difference scheme for steady, supersonic, two-dimensional, compressible flow of real gases

A finite difference scheme is presented for the solution of the two-dimensional equations of steady, supersonic, compressible flow of real gases. The scheme incorparates numerical characteristic decomposition, is shock-capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supersonic in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

A finite element simulation of micro-mechanical frictional behaviour in metal forming

Friction is a critical factor for sheet metal forming (SMF). The Coulomb friction model is usually used in most finite element (FE) simulation for SMF. However, friction is a function of the local contact deformation conditions, such as local pressure, roughness and relative velocity. Frictional behaviour between contact surfaces can be based on three cases: boundary, hydrodynamic and mixed lubrication. In our microscopic friction model based on the finite element method (FEM), the case of dry contact between sheet and tool has been considered. In the view of microscopic geometry, roughness depends upon amplitude and wavelength of surface asperities of sheet and tool. The mean pressure applied on the surface differs from the pressure over the actual contact area. The effect of roughness (microscopic geometric condition) and relative speed of contact surfaces on friction coefficient was examined in the FE model for the microscopic friction behaviour. The analysis was performed using an explicit FE formulation. In this study, it was found that the roughness of deformable sheet decreases during sliding and the coefficient of friction increases with increasing roughness of contact surfaces. Also, the coefficient of friction increases with the increase of relative velocity and adhesive friction coefficient between contact surfaces.

Finite element simulation of deformation processes of micro-components

The aim of this paper is to improve the understanding of deformation of micro medical needle and thread during assembly and then to develop an economical and flexible deformation method. Therefore, the swaging process is computationally simulated with the finite element method in this paper. A commercially available explicit nonlinear finite element analysis code, LS-Dyna, is used to model the 3-D deformation and contact problem. As the firmness of the assembly on the needle depends on the contact force and friction, the contact and the slide between the needle and thread are taken into account in the simulation. The general surface-to-surface contact algorithm (STS) is used to simulate the contact. The paper provides an insight into the deformation of the micro products.

Use of artificial neural networks as explicit finite difference operators

Results of a numerical exercise, substituting a numerical operator by an artificial neural network (ANN) are presented in this paper. The numerical operator used is the explicit form of the finite difference (FD) scheme. The FD scheme was used to discretize the one-dimensional transport equation, which included both the advection and dispersion terms. Inputs to the ANN are the FD representation of the transport equation, and the concentration was designated as the output. Concentration values used for training the ANN were obtained from analytical solutions. The numerical operator was reconstructed from a back calculation of the weights of the ANN. Linear transfer functions were used for this purpose. The ANN was able to accurately recover the velocity used in the training data, but not the dispersion coefficient. This capability was improved when numerical dispersion was taken into account; however, it is limited to the condition: C/P<0.5 , where C is the Courant number and P , the Peclet number (i.e., the restriction imposed by the Neumann stability condition).

BOUND HYDROGENIC STATES IN A MAGNETIC FIELD: A FINITE-DIFFERENCE APPROACH

A finite-difference scheme is used to calculate bound electronic states of an electron in a hydrogen atom subject to a magnetic field. The numerical results are in good agreement with exact results, in the absence of the magnetic field, and with a two-parameters variational calculation, when the magnetic field is applied.

Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.

Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Finite element simulation of a local scale air quality model over complex terrain

[EN]In this paper we propose a finite element method approach for modelling the air quality in a local scale over complex terrain. The area of interest is up to tens of kilometres and it includes pollutant sources. The proposed methodology involves the generation of an adaptive tetrahedral mesh, the computation of an ambient wind field, the inclusion of the plume rise effect in the wind field, and the simulation of transport and reaction of pollutants. We apply our methodology to simulate a fictitious pollution episode in La Palma island (Canary Island, Spain)...

Adaptive finite element simulation of stack pollutant emissions over complex terrains

[EN]A three-dimensional finite element model for the pollutant dispersion is presented. In these environmental processes over a complex terrain, a mesh generator capable of adapting itself to the topographic characteristics is essential. The first stage of the model consists on the construction of an adaptive tetrahedral mesh of a rectangular region bounded in its lower part by the terrain and in its upper part by a horizontal plane. Once the mesh is constructed, an adaptive local refinement of tetrahedra is used in order to capture the plume rise. Wind measurements are used to compute an interpolated wind field, that is modified by using a mass-consistent model and perturbing its vertical component to introduce the plume rise effect...

Three dimensional finite element simulation of polymer melting and flow in a single-screw extruder : optimization of screw channel geometry

Single-screw extrusion is one of the widely used processing methods in plastics industry, which was the third largest manufacturing industry in the United States in 2007 [5]. In order to optimize the single-screw extrusion process, tremendous efforts have been devoted for development of accurate models in the last fifty years, especially for polymer melting in screw extruders. This has led to a good qualitative understanding of the melting process; however, quantitative predictions of melting from various models often have a large error in comparison to the experimental data. Thus, even nowadays, process parameters and the geometry of the extruder channel for the single-screw extrusion are determined by trial and error. Since new polymers are developed frequently, finding the optimum parameters to extrude these polymers by trial and error is costly and time consuming. In order to reduce the time and experimental work required for optimizing the process parameters and the geometry of the extruder channel for a given polymer, the main goal of this research was to perform a coordinated experimental and numerical investigation of melting in screw extrusion. In this work, a full three-dimensional finite element simulation of the two-phase flow in the melting and metering zones of a single-screw extruder was performed by solving the conservation equations for mass, momentum, and energy. The only attempt for such a three-dimensional simulation of melting in screw extruder was more than twenty years back. However, that work had only a limited success because of the capability of computers and mathematical algorithms available at that time. The dramatic improvement of computational power and mathematical knowledge now make it possible to run full 3-D simulations of two-phase flow in single-screw extruders on a desktop PC. In order to verify the numerical predictions from the full 3-D simulations of two-phase flow in single-screw extruders, a detailed experimental study was performed. This experimental study included Maddock screw-freezing experiments, Screw Simulator experiments and material characterization experiments. Maddock screw-freezing experiments were performed in order to visualize the melting profile along the single-screw extruder channel with different screw geometry configurations. These melting profiles were compared with the simulation results. Screw Simulator experiments were performed to collect the shear stress and melting flux data for various polymers. Cone and plate viscometer experiments were performed to obtain the shear viscosity data which is needed in the simulations. An optimization code was developed to optimize two screw geometry parameters, namely, screw lead (pitch) and depth in the metering section of a single-screw extruder, such that the output rate of the extruder was maximized without exceeding the maximum temperature value specified at the exit of the extruder. This optimization code used a mesh partitioning technique in order to obtain the flow domain. The simulations in this flow domain was performed using the code developed to simulate the two-phase flow in single-screw extruders.