Singularity programming: A numerical technique for determining the effect of singularities in finite difference solutions illustrated by application to plane elastic problems

1973 ◽  
Vol 6 (3) ◽  
pp. 367-380 ◽  
Author(s):  
A. F. Emery ◽  
C. M. Segedin
Keyword(s):  
Finite Difference ◽  
Numerical Technique ◽  
Plane Elastic Problems

Finite Difference Time Domain Simulations of Hybrid Neurotransducers Based Optical Microlasers

2020 ◽  
Author(s):  
Maurizio Manzo ◽  
Omar Cavazos
Keyword(s):  
Finite Difference ◽  
Chronic Traumatic Encephalopathy ◽  
Numerical Technique ◽  
Well Being ◽  
Infrared Light ◽  
Neuron Activity ◽  
Living Matter ◽  
Brain Functions ◽  
Laser Modes ◽  
The Brain

Abstract Different pathologies such as Alzheimer’s, Parkinson’s, Wilson’s diseases, and chronic traumatic encephalopathy due to blasts and impacts affect the brain functions altering the neuronal electrical activity. An important aspect of the brain study is the use of non-invasive, non-surgical methodologies that are suitable to the well-being of the patients. Only a portion of the electromagnetic field can be detected by applying sensors outside the scalp; in addition, surgery is often involved if sensors are applied in the subcutaneous region of the skull. Optical techniques applied to biomedical research and diagnostics have been spread during the last decades. For example, near infrared light (NIR) of spectral range goes from 800 nm to 1300 nm, it is harmless radiation for the living tissue, and can penetrate the living matter in depth as, it turns out that most of the living matter is transparent to the NIR light. Optical microlasers have been recently proposed as neurotransducers for minimally invasive neuron activity detection for the next generation of brain-computer interface (BCI) systems. They are lightweight, require low power consumption and exhibit low latency. This novel sensor that can be made of biocompatible material is coupled with a voltage sensitive dye; the fluorescence of the dye, which is excited by an external light source, is used to generate optical (laser) modes. Any variation in the neurons’ membrane electric potential via evanescent field’s perturbation turn affect the shifting of these laser modes. In order to reduce the energy required to power these devices and to improve their optical emission, metal nanoparticles can be coupled in order to use their plasmonic effect. In this paper, finite-difference timedomain (FDTD) numerical technique is used to analyze the performances on a dye-doped microlaser. Purcell effect and resonant wavelengths are observed.

Strain rate sensitivity of a mild steel at room temperature and strain rates of up to 105s−1

1980 ◽  
Vol 15 (4) ◽  
pp. 201-207 ◽  
Author(s):  
M S J Hashmi
Keyword(s):  
Finite Difference ◽  
Mild Steel ◽  
Strain Rate ◽  
Strain Hardening ◽  
Strain Rate Sensitivity ◽  
Elastic Strain ◽  
Room Temperature ◽  
Numerical Technique ◽  
Rate Sensitivity ◽  
Strain Rates

Experimental results on a mild steel are reported from ballistics tests which gave rise to strain rates of up to 105 s−1. A finite-difference numerical technique which incorporates material inertia, elastic-strain hardening and strain-rate sensitivity is used to establish the strain-rate sensitivity constants p and D in the equation, σ4 = σ1 (1+(∊/D)1/ p). The rate sensitivity established in this study is compared with those reported by other researchers.

Fractional Chebyshev Finite Difference Method for Solving the Fractional-Order Delay BVPs

2015 ◽  
Vol 12 (06) ◽  
pp. 1550033 ◽  
Author(s):  
M. M. Khader
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Fractional Order ◽  
Difference Method ◽  
Matrix Method ◽  
Fractional Derivatives ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Operational Matrix Method ◽  
Chebyshev Finite Difference Method

In this paper, we implement an efficient numerical technique which we call fractional Chebyshev finite difference method (FChFDM). The fractional derivatives are presented in terms of Caputo sense. The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a nonuniform finite difference scheme. The error bound for the fractional derivatives is introduced. We used the introduced technique to solve numerically the fractional-order delay BVPs. The application of the proposed method to introduced problem leads to algebraic systems which can be solved by an appropriate numerical method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

scholarly journals Comparative analysis of Rectangular Plate by Finite element method and Finite Difference Method

2021 ◽  
Vol 9 (9) ◽  
pp. 1397-1398
Author(s):  
Dr. A. R. Gupta
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Comparative Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Rectangular Plate ◽  
Difference Method ◽  
Numerical Technique ◽  
Element Analysis ◽  
Element Method

Abstract: Plates are commonly used to support lateral or vertical loads. Before the design of such a plate, analysis is performed to check the stability of plate for the proposed load. There are several methods for this analysis. In this research, a comparative analysis of rectangular plate is done between Finite Element Method (FEM) and Finite Difference Method (FDM). The plate is considered to be subjected to an arbitrary transverse uniformly distributed loading and is considered to be clamped at the two opposite edges and free at the other two edges. The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It is also referred to as finite element analysis (FEA). FEM subdivides a large problem into smaller, simpler, parts, called finite elements. The work covers the determination of displacement components at different points of the plate and checking the result by software (STAAD.Pro) analysis. The ordinary Finite Difference Method (FDM) is used to solve the governing differential equation of the plate deflection. The proposed methods can be easily programmed to readily apply on a plate problem. Keywords: Arbitrary, FEM, FDM, boundary.

scholarly journals One-dimensional model for the computation of unsteady salinity intrusion in a river

1982 ◽  
Vol 4 (3) ◽  
pp. 1-15
Author(s):  
Nguyen Van Diep ◽  
Nguyen Tat Dac ◽  
Tran Ngoc Duyet
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Numerical Technique ◽  
Momentum Equation ◽  
Transient Condition ◽  
Salinity Intrusion ◽  
Dimensional Model ◽  
One Dimensional ◽  
Tidal Motion ◽  
Implicit Finite Difference

The study is concerned with the development of a predictive, on – dimensional. Mathematical model for the salinity intrusion in a river. This is accomplished by means of simultaneous weighted implicit finite difference solutions to the salt balance equation and to the continuity and momentum equation which definite the tidal motion. It is shown that the boundary condition on salinity at downstream can be specified by using one condition during the flood tide and another condition during the ebb-tide. The resulting mathematical model, as solved by a finite-difference numerical technique can be used in a predictive manner for transient condition of downstream, surface elevation and time-varying fresh water discharges at upstream.

scholarly journals Numerical solution of free-boundary problems in fluid mechanics. Part 1. The finite-difference technique

1984 ◽  
Vol 148 ◽  
pp. 1-17 ◽  
Author(s):  
G. Ryskin ◽  
L. G. Leal
Keyword(s):  
Finite Difference ◽  
Free Boundary ◽  
Fluid Mechanics ◽  
Free Boundary Problems ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Boundary Problems ◽  
Boundary Shape ◽  
Curvilinear Coordinate ◽  
Ultimate Equilibrium

We present here a brief description of a numerical technique suitable for solving axisymmetric (or two-dimensional) free-boundary problems of fluid mechanics. The technique is based on a finite-difference solution of the equations of motion on an orthogonal curvilinear coordinate system, which is also constructed numerically and always adjusted so as to fit the current boundary shape. The overall solution is achieved via a global iterative process, with the condition of balance between total normal stress and the capillary pressure at the free boundary being used to drive the boundary shape to its ultimate equilibrium position.

Controlling Numerical Dispersion by Variably Timed Flux Updating in One Dimension

1982 ◽  
Vol 22 (03) ◽  
pp. 399-408 ◽  
Author(s):  
R.G. Larson
Keyword(s):  
Finite Difference ◽  
Truncation Error ◽  
Hyperbolic Equations ◽  
Numerical Technique ◽  
Material Balance ◽  
Three Dimensions ◽  
Numerical Dispersion ◽  
Point Tracking ◽  
Multidimensional Problems ◽  
Grid Orientation

Abstract The one-dimensional (1D) material balance equations for multiphase multicomponent transport in porous media can be cast into forms, analogous to characteristic equations, that express explicitly the velocities at which fixed values of concentration are propagated. Use of these concentration-velocity equations to control the frequency with which component fluxes from finite-difference gridblocks ate updated leads to greatly reduced numerical dispersion, as demonstrated in miscible flooding, waterflooding, surfactant flooding, and other example problems. Introduction Accurate numerical simulation of enhanced oil-recovery processes, such as CO2, surfactant, thermal, or caustic flooding can involve calculations of phase behavior, interfacial tension, relative permeabilities, viscosities, heat and mass transfer, and even chemical reactions, thereby requiring considerable computational effort for each meshpoint or gridblock at each timestep. It is therefore impractical to resolve the steep concentration or thermal gradients often present in these processes by resorting to ultrafine meshes. Because the mathematical description of such processes is often unavoidably complex, it is important that the numerical technique be simple and ruggedly insensitive to the details of the process description, if one is to avoid becoming ensnarled in cumbersome and tedious programming and debugging.Although the finite-difference method's simplicity is its great advantage, its accuracy is seriously deficient, at least when one is using the simplest and most obvious discretizations. Central-difference discretization leads to artificial oscillations and overshoot, and upstream differencing leads to artificial smearing of sharp fronts-i.e., numerical dispersion or truncation error. Upstream difference solutions in two or three dimensions often show a significant dependence on grid orientation. Suggested improvements in the finite-difference technique, such as "transfer of overshoot," "truncation error analysis," or "two-point upstream weighting," still have significant numerical dispersion, grid orientation or oscillation errors.The method of characteristics, or point tracking, incurs no numerical dispersion or overshoot errors, but for general multicomponent, multidimensional problems, computer programs based on these techniques can become labyrinthine in their complexity.The finite-element, or variational, methods hold the potential of significantly reducing overshoot and/or numerical dispersion below that produced by finite difference, but implementation is considerably more complicated and time-consuming.The method of random choice, a technique developed for solving sets of multidimensional hyperbolic equations that appear in gas dynamics, recently has been employed in reservoir simulation. This method is somewhat akin to point tracking, propagating discontinuous fronts without smearing or overshoot errors.A new numerical technique is presented here that has the form and simplicity of finite difference, but utilizes variably timed flux updating (VTU) to gain a considerable improvement in accuracy. The technique is potentially applicable to general multicomponent, multidimensional problems. In this and a companion paper (see Pages 409-419), however, the technique is restricted to problems governed by the following equations. SPEJ P. 399^

Numerical Modeling of Turbulent Surface Wave Motion Using a Coupled Boundary Element-Finite Difference Technique

2008 ◽  
Author(s):  
Mirmosadegh Jamali
Keyword(s):  
Surface Wave ◽  
Finite Difference ◽  
Wave Motion ◽  
Turbulence Modeling ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Solid Surfaces ◽  
Mixing Length ◽  
Finite Difference Technique ◽  
Mixing Length Theory

In this paper an effective numerical technique is presented to model turbulent motion of a standing surface wave in a tank. The equations of motion for turbulent boundary layers at the solid surfaces are coupled with the potential flow in the bulk of the fluid, and a mixed BEM-finite difference technique is used to obtain the wave and boundary layer characteristics. A mixing-length theory is used for turbulence modeling. The results are compared with previous experimental data. Although the technique is presented for a standing surface wave, it can be easily applied to other free surface problems.

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