Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
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Papers
Book•
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1 Jan 1975
TL;DR: In this article, the theory and applications of the analytical techniques used in finding stresses in highway and other bridge decks are discussed and an approximate method of determination of bending moments for initial design is described.
Abstract: The book presents the theory and applications of the analytical techniques used in finding stresses in highway and other bridge decks. Current trends in bridge design and construction are discussed and are followed by the various analytical methods. The plate method is dealt with, initially by the basic derivation and solution of the plate equation. A chapter is devoted to the determination of the equivalent plate rigidities of various representative types of bridge deck. An approximate method of determination of bending moments for initial design is described. Various special applications of orthotropic plate theory are covered and the finite difference method for plates is described, including a summary of the dynamic relaxation method. The last four chapters deal with the stiffness method and its application: grillage and space frame analysis, the folded plate method, the finite element method, and the finite strip method. The book is intended for use by bridge designers and students with a particular interest in bridge engineering. /TRRL/
130 citations
TL;DR: In this paper, a class of gas lubricated foil thrust bearings has been investigated analytically utilizing a novel approach which combines Finite Difference (FD) and Finite Element (FE) methods.
Abstract: Load performance of gas lubricated, compliant surface foil thrust bearings has an interlocking relationship with the compliance of the bearing and hydrodynamics of convergent wedge surface. Compliance of the bearing consists of supporting spring elements (elastic foundation) and a smooth elastic top foil. In this paper, a class of gas lubricated foil thrust bearings has been investigated analytically utilizing a novel approach which combines Finite Difference (FD) and Finite Element (FE) methods. Solution of the governing hydrodynamic equations dealing with compressible fluid is coupled with the structural resiliency of the foil bearing surfaces. FD method is utilized for hydrodynamic analysis while FE is used to model structural resiliency. Influence coefficients were generated to address the elasticity effects of combined top foil and elastic foundation on the hydrodynamics of thrust bearing, and were used to expedite the numerical solution. Within 2 to 3 iterations the convergence criterion was reached. The overall program logic proved to be an efficient technique to deal with the complex structural compliance of various foil bearing. Case study has been conducted and sample solutions are provided. Unlike prior analytical investigations, the essential effect of the top foil on the performance of the bearing has been elucidated.
130 citations
TL;DR: In this paper, an active and efficient method of including frequency-dependent conductor losses into the time-domain solution of the multiconductor transmission line equations is presented, which is shown that the usual A+B/spl radic/s representation of these frequencydependent losses is not valid for some practical geometries, and a computationally efficient method for improving this representation in the finite-difference time domain (FDTD) solution method is given and is verified using the conventional TDFD solution technique.
Abstract: An active and efficient method of including frequency-dependent conductor losses into the time-domain solution of the multiconductor transmission line equations is presented. It is shown that the usual A+B/spl radic/s representation of these frequency-dependent losses is not valid for some practical geometries. The reason for this the representation of the internal inductance the at lower frequencies. A computationally efficient method for improving this representation in the finite-difference time-domain (FDTD) solution method is given and is verified using the conventional time-domain to frequency-domain (TDFD) solution technique.
130 citations
TL;DR: In this article, a theoretical examination of the approximation of several difference operators, both implicit and explicit, is presented and the stability of these schemes is examined empirically for flow over a plane with critical depth downstream boundary condition and a zero inflow upstream boundary condition.
Abstract: The quasi-linear partial differential equations known as the shallow-water equations describe the flow of water in open channels or over sloping planes (overland flow). Because no analytic solution exists for these equations, finite-difference methods must be used to obtain solutions. Formulation of finite-difference schemes involves consideration of the convergence of the finite-difference solutions to the true solution of the equation. A theoretical examination of the approximation of several difference operators, both implicit and explicit, is presented and the stability of these schemes is examined empirically for flow over a plane with critical depth downstream boundary condition and a zero inflow upstream boundary condition. A finite-difference scheme based on the method of characteristics was found to be satisfactory in many cases. Explicit methods were found to be not suitable for this problem except in some special cases.
130 citations
TL;DR: The GFD explicit formulae developed to obtain the different derivatives of the pde's are based on the existence of a positive definite matrix that it is obtained using moving least squares approximation and Taylor series development.
129 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |