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.
Papers published on a yearly basis
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Papers
TL;DR: In this article, a finite difference method to solve the incompressible Navier-Stokes equations in cylindrical geometries is presented based upon the use of mimetic discrete first-order operators (divergence, gradient, curl), i.e. operators which satisfy in a discrete sense most of the usual properties of vector analysis in the continuum case.
85 citations
TL;DR: In this paper, a low-Mach-number model was used to predict the steady-state, acoustically generated temperature gradient across a two-dimensional couple and to analyze its dependence on the amplitude of the prevailing resonant wave.
85 citations
TL;DR: In this article, a semi-analytic finite difference method was extended to the vibration and stability analysis of stiffened plates, which essentially consists of substituting the displacement function satisfying boundary conditions along two opposite edges into the free vibration/stability equations of the stiffened plate and then, by using suitable transformation, they are reduced to ordinary differential equations with constant coefficients.
85 citations
TL;DR: In this paper, a numerical technique suitable for solving axisymmetric, unsteady free-boundary problems in fluid mechanics is presented, based on a finite-difference solution of the equations of motion on a moving orthogonal curvilinear coordinate system, which is constructed numerically and adjusted to fit the boundary shape at any time.
Abstract: A brief description of a numerical technique suitable for solving axisymmetric, unsteady free‐boundary problems in fluid mechanics is presented. The technique is based on a finite‐difference solution of the equations of motion on a moving orthogonal curvilinear coordinate system, which is constructed numerically and adjusted to fit the boundary shape at any time. The initial value problem is solved using a fully implicit first‐order backward time differencing scheme in order to insure numerical stability. As an example of application, the unsteady deformation of a bubble in a uniaxial extensional flow for Reynolds numbers is considered in the range of 0.1≤R≤100. The computation shows that the bubble extends indefinitely if the Weber number is larger than a critical value (W>Wc). Furthermore, it is shown that a bubble may not achieve a stable steady state even at subcritical values of Weber number if the initial shape is sufficiently different from the steady shape. Finally, potential‐flow solutions as an ...
85 citations
Book•
1 Jan 1994
TL;DR: In this article, the authors proposed a Compact Combination of the Finite Element, Linear Iteration and Finite Difference Methods for solving the one-dimensional Bar Model Problem (Principle of Virtual Work).
Abstract: Introduction. 1. One-Dimensional Bar Model Problem (Principle of Virtual Work). 2. Spatial Discretisation by the Finite Element Method. 3. Solution of Nonlinearities by the Linear Iteration Method. 4. Time Integration by the Finite Difference Method. 5. Compact Combination of the Finite Element, Linear Iteration and Finite Difference Methods. 6. Two and Three-Dimensional Deformable Solids. Conclusion. Bibliography. Appendix A: List of Symbols. Appendix B: Exercises. Index.
85 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |