Search results for "finite difference"

Efficient finite-difference scheme for solving some heat transfer problems with convection in multilayer media

2000

Abstract An efficient finite-difference method for solving the heat transfer equation with piecewise discontinuous coefficients in a multilayer domain is developed. The method may be considered as a generalization of the finite-volumes method for the layered systems. We apply this method with the aim to reduce the 3D or 2D problem to the corresponding series of 2D or 1D problems. In the case of constant piecewise coefficients, we obtain the exact discrete approximation of the steady-state 1D boundary-value problem.

Introductory Quantum Physics Courses using a LabVIEW multimedia module

2007

We present the development of a LabVIEW multimedia module for introductory Quantum Physics courses and our experience in the use of this application as an educational tool in learning methodologies. The program solves the Time Dependent Schrodinger Equation for arbitrary potentials. We describe the numerical method used for solving this equation, as well as some mathematical tools employed to reduce the calculation time and to obtain more accurate results. As an illustration, we present the evolution of a wave packet for three different potentials: the repulsive barrier potential, the repulsive step potential, and the harmonic oscillator. This application has been successfully integrated in…

The Mathematical Modeling of Ca And Fe Distribution In Peat Layers

2015

Bogs have been formed by an accumulation of peat - a light brown-to-black organic material, built up from partial decomposition of mosses and other bryophytes, sedges, grasses, shrubs, or trees under waterlogged conditions. The total peatlands area in Latvia covers 698 918 ha or 10.7% of the entire territory. Knowledge’s of peat metals content are important for any kind of peat using. Experimental determination of metals in peat is very long and expensive work. Using experimental data mathematical model for calculation of concentrations of metals in different points for different layers can help to very easy and fast to find approximately concentration of metals or trace elements. The resul…

Hybrid WENO schemes for polydisperse sedimentation models

2015

International audience; Polydisperse sedimentation models can be described by a strongly coupled system of conservation laws for the concentration of each species of solids. Typical solutions for the sedimentation model considered for batch settling in a column include stationary kinematic shocks separating layers of sediment of different composition. This phenomenon, known as segregation of species, is a specially demanding task for numerical simulation due to the need of accurate numerical simulations. Very high-order accurate solutions can be constructed by incorporating characteristic information, available due to the hyperbolicity analysis made in Donat and Mulet [A secular equation fo…

APPLICATION OF 3‐D FINITE DIFFERENCE METHOD FOR INDUCTANCE CALCULATION OF AIR‐CORE COILS SYSTEM

1994

The paper deals with the inductance calculation of air‐core coils system by means of 3‐D analysis of magnetic field of the coils with rectangular cross‐section. The possibility of mutual and self‐inductance calculation is presented. For magnetic field calculation, the Finite Difference Method with application of fast calculating procedures was applied. The method of calculation has been verified by experiments. The obtained difference between calculating and measurement results is equal to a few percent. The computer program is usefull especially for asymmetrical configuration of the coils.

A Finite Difference Model of a PV-PCM System

2012

Abstract The performances of a photovoltaic panel (PV) are defined according to the “peak power” that identifies the maximum electric power supplied by the panel when it receives an insolation of 1 kW/m2 and the temperature of the cell is maintained at 25 °C. These conditions are only nominal since the solar radiation has a variable intensity and also the panel is subjected to thermal excursions; due to these reasons the real power efficiency of the panel is considerably lower than that obtainable in the nominal conditions. The study focused on assessing a method to reduce the peak temperatures of PV systems using Phase Change Materials (PCM). To this aim it was created a numerical model ca…

A Comparison and Survey of Finite Difference Methods for Pricing American Options Under Finite Activity Jump-Diffusion Models

2012

Partial-integro differential formulations are often used for pricing American options under jump-diffusion models. A survey on such formulations and numerical methods for them is presented. A detailed description of six efficient methods based on a linear complementarity formulation and finite difference discretizations is given. Numerical experiments compare the performance of these methods for pricing American put options under finite activity jump models.

A comparison of numerical surface topography calculations in geodynamic modelling: an evaluation of the ‘sticky air’ method

2012

SUMMARY Calculating surface topography in geodynamic models is a common numerical problem. Besides other approaches, the so-called ‘sticky air’ approach has gained interest as a free-surface proxy at the top boundary. The often used free slip condition is thereby vertically extended by introducing a low density, low viscosityfluid layer. This allows the air/crust interface to behave in a similar manner to a true free surface. We present here a theoretical analysis that provides the physical conditions under which the sticky air approach is a valid approximation of a true free surface. Two cases are evaluated that characterize the evolution of topography on different timescales: (1) isostati…

A Numerical Approach to Finite Journal Bearings Lubricated With Ferrofluid

1987

Several cases of cylindrical bearings lubricated with ferrofluid are examined by means of a finite-difference numerical procedure. The subregion of cavitation is determined by imposing mass conservation across the “rupture” and “reformation” boundaries of the complete film. The examined cases refer to bearings confined by sealing rings formed by the lubricant itself, for which there is no need of external supply. In each case the most significant parameters are calculated and it is possible to see that the use of these bearings is favorable when speeds are low, clearances large, and loads light, because in such conditions the magnetic effects are comparable with the pure hydrodynamic ones a…

2020

Abstract. Quantifying the hydraulic properties of single fractures is a fundamental requirement to understand fluid flow in fractured reservoirs. For an ideal planar fracture, the effective flow is proportional to the cube of the fracture aperture. In contrast, real fractures are rarely planar, and correcting the cubic law in terms of fracture roughness has therefore been a subject of numerous studies in the past. Several empirical relationships between hydraulic and mechanical aperture have been proposed based on statistical variations of the aperture field. However, often, they exhibit non-unique solutions, attributed to the geometrical variety of naturally occurring fractures. In this st…