Search results for "Finite difference"
showing 10 items of 122 documents
Transmission properties at microwave frequencies of two-dimensional metallic lattices
1999
The transmission properties of different metallic photonic lattices (square and rectangular) have been experimentally studied. A numerical algorithm based on time domain finite differences has been used for simulating these photonic structures. The introduction of defects in the two-dimensional metallic lattice modifies its transmission spectrum. If metal rods are eliminated from (or added to) the lattice, extremely narrow peaks are observed at some particular frequencies below (or above) the band pass edge. Vicente.Such@uv.es ; Enrique.Navarro@uv.es
Finite difference analysis of the thermal behaviour of coated tools in orthogonal cutting of steels
2004
Abstract Temperature measurement and prediction have been a major focus of machining for several decades but now this problem became more important due to the wider use of advanced cutting tool coatings. Practically, there is a lack of simulation programs for prediction of the temperatures in the cutting zone when machining with differently coated cutting tools. In all literature items cited the finite difference methods (finite difference approaches) were used to find the distribution of temperature inside the uncoated tool body or along the tool–chip interface for continuous (turning) and interrupted (milling) machining processes. The algorithm applied overcomes this limit. In this study,…
SOIL IONIZATION DUE TO HIGH PULSE TRANSIENT CURRENTS LEAKED BY EARTH ELECTRODES
2009
This paper proposes a numerical model of the soil ionization phenomena that can occur when earth electrodes are injected by high pulse transient currents, as the one associated with a direct lightning stroke. Based on finite difference time domain numerical scheme, this model ascribes the electrical breakdown in the soil to the process of discharge in the air. In fact, as soon as the local electric field overcomes the electrical strength, the air in the voids trapped among soil particles is ionized, and the current is conducted by ionized plasma paths locally grown. The dimension of these ionized air channels is strictly dependent upon the local temperature. Thus, a local heat balance is en…
FINITE DIFFERENCE METHOD-BASED SIMULATION OF TEMPERATURE FIELDS FOR APPLICATION TO ORTHOGONAL CUTTING WITH COATED TOOLS
2005
ABSTRACT A finite difference method was proposed to model the effect of a variety of tool coatings on the magnitude and distribution of temperatures through the tool-chip contact region and the coating/substrate boundaries. For each workpiece-tool pair tested the intensity of uniformly distributed heat flux and relevant analytically obtained values of the heat partition coefficient were assumed to change with variations of cutting speed and the corresponding friction. In this case the simulation of an orthogonal machining of AISI 1045 steel was performed using special computing algorithm with elementary balances of induced energies (MBE). It is concluded that the temperature contours obtain…
Transport properties of heterogeneous materials. Combining computerised X-ray micro-tomography and direct numerical simulations
2009
Feasibility of a method for finding flow permeability of porous materials, based on combining computerised X-ray micro-tomography and numerical simulations, is assessed. The permeability is found by solving fluid flow through the complex 3D pore structures obtained by tomography for actual material samples. We estimate overall accuracy of the method and compare numerical and experimental results. Factors contributing to uncertainty of the method include numerical error arising from the finite resolution of tomographic images and the rather small sample size available with the present tomographic techniques. The total uncertainty of computed values of permeability is, however, not essentiall…
Further experiences on unsteady seepage flow
1973
The present paper describes the results of a study on the unsteady flow in a horizontal homogeneous filter, which is accomplished when the level of the reservoir that recharges the filter is instantly drawn up. This study was carried out at the University of Palermo Institute of Hydraulics as a part of a research program concerning artificial recharge of ground water and the geotechnical problems involving the stability of porous media subject to the variations of surrounding pressures. A numerical procedure, aiming at solving the equation of Boussinesq by a finite difference method, was adopted and an electronic computer was used. A Hele-Shaw filter model was used to carry out several expe…
Determination of Torsional Stresses in Shafts: From Physical Analogies to Mathematical Models
2015
This paper presents the historical development of methods used for the study of torsional stresses in shafts. In particular, the paper covers both analog methods, especially those based on electrical analogies proposed circa 1925, and numerical methods, especially finite difference methods (FDM), finite element methods (FEM) and boundary element methods (BEM).
On Mathematical Modelling of Metals Distribution in Peat Layers
2014
In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in multilayered domain. We consider the metals Fe and Ca concentration in the layered peat blocks. Using experimental data the mathematical model for calculation of concentration of metals in different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations (PDEs) of second order with piece-wise diffusion coefficients in the layered domain. We develop here a finite-difference method for solving of a problem of one, two and three peat blocks with periodica…
An Iterative Method for Pricing American Options Under Jump-Diffusion Models
2011
We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou's and Merton's jump-diffusion models show that the resulting iteration converges rapidly.
An IMEX-Scheme for Pricing Options under Stochastic Volatility Models with Jumps
2014
Partial integro-differential equation (PIDE) formulations are often preferable for pricing options under models with stochastic volatility and jumps, especially for American-style option contracts. We consider the pricing of options under such models, namely the Bates model and the so-called stochastic volatility with contemporaneous jumps (SVCJ) model. The nonlocality of the jump terms in these models leads to matrices with full matrix blocks. Standard discretization methods are not viable directly since they would require the inversion of such a matrix. Instead, we adopt a two-step implicit-explicit (IMEX) time discretization scheme, the IMEX-CNAB scheme, where the jump term is treated ex…