Search results for "Finite difference method"
showing 10 items of 63 documents
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…
A Non-Local Two Dimensional Foundation Model
2012
Classical foundation models such as the Pasternak and the Reissner models have been recently reformulated within the framework of non-local mechanics, by using the gradient theory of elasticity. To contribute to the research effort in this field, this paper presents a two-dimensional foundation model built by using a mechanically based non-local elasticity theory, recently proposed by the authors. The foundation is thought of as an ensemble of soil column elements resting on an elastic base. It is assumed that each column element is acted upon by a local Winkler-like reaction force exerted by the elastic base, by contact shear forces and volume forces due, respectively, to adjacent and non-…
Drying of shrinking cylinder-shaped bodies
1998
Abstract A mathematical model has been developed for the prediction of sample temperature, average moisture and moisture distribution in a cylinder-shaped solid during the drying process. The effect of shrinkage was taken into account. The macroscopic heat balance and the microscopic mass balance combined with Fick's law were simultaneously solved using the Runge-Kutta-Merson method and a numerical finite difference method. The effective diffusion coefficient was expressed as a function of sample temperature and local moisture content. Using an experimental drying curve determined at 90 °C, the diffusional equation was identified for broccoli stems, and was used to predict the average and l…
Physical modeling of heat and moisture transfer in wet bio-sourced insulating materials.
2018
Simultaneous heat and moisture transfers in bio-sourced insulating materials are significant phenomena in thermal metrology. The present study focuses on these phenomena by experimental and numerical approaches based on the asymmetric hot-plate method. In this paper, a bio-sourced insulating material based on flax fibers is developed. The thermal and hygric properties of the sample are then investigated in the humid atmosphere. The temperature is maintained at 30 °C, and the relative humidity varies between 30% and 90% RH. A physics-based model of simultaneous heat and moisture transfer is developed for thermal conductivity estimation. This model is discretized with finite difference method…
Energy-Stable Numerical Schemes for Multiscale Simulations of Polymer–Solvent Mixtures
2017
We present a new second-order energy dissipative numerical scheme to treat macroscopic equations aiming at the modeling of the dynamics of complex polymer–solvent mixtures. These partial differential equations are the Cahn-Hilliard equation for diffuse interface phase fields and the Oldroyd-B equations for the hydrodynamics of the polymeric mixture. A second-order combined finite volume/finite difference method is applied for the spatial discretization. A complementary approach to study the same physical system is realized by simulations of a microscopic model based on a hybrid Lattice Boltzmann/Molecular Dynamics scheme. These latter simulations provide initial conditions for the numerical…
High-quality discretizations for microwave simulations
2016
We apply high-quality discretizations to simulate electromagnetic microwaves. Instead of the vector field presentations, we focus on differential forms and discretize the model in the spatial domain using the discrete exterior calculus. At the discrete level, both the Hodge operators and the time discretization are optimized for time-harmonic simulations. Non-uniform spatial and temporal discretization are applied in problems in which the wavelength is highly-variable and geometry contains sub-wavelength structures. peerReviewed