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 paper, high-order compact finite difference schemes for two-dimensional convection-diffusion-type differential equations with constant and variable convection coefficients are derived and tested against standard model problems, including a Navier-Stokes application.
Abstract: High-order compact finite difference schemes for two-dimensional convection-diffusion-type differential equations with constant and variable convection coefficients are derived. The governing equations are employed to represent leading truncation terms, including cross-derivatives, making the overall O(h4) schemes conform to a 3 × 3 stencil. We show that the two-dimensional constant coefficient scheme collapses to the optimal scheme for the one-dimensional case wherein the finite difference equation yields nodally exact results. The two-dimensional schemes are tested against standard model problems, including a Navier-Stokes application. Results show that the two schemes are generally more accurate, on comparable grids, than O(h2) centred differencing and commonly used O(h) and O(h3) upwinding schemes.
86 citations
TL;DR: In this paper, a semicoarsening multigrid algorithm for solving the finite difference discretization of symmetric and nonsymmetric, two-and three-dimensional elliptic partial differential equations with highly discontinuous and anisotropic coefficients is presented.
Abstract: The purpose of this paper is to present a semicoarsening multigrid algorithm for solving the finite difference discretization of symmetric and nonsymmetric, two- and three-dimensional elliptic partial differential equations with highly discontinuous and anisotropic coefficients. The discrete equations are assumed to be defined on a logically rectangular grid, obtained possibly through grid generation for a problem defined on an irregular domain. The basic algorithm is described along with some modifications which are designed to improve its efficiency and robustness for certain types of problem cases. FORTRAN codes that implement the two- and three-dimensional semicoarsening multigrid algorithms are described briefly, and numerical results are presented.
86 citations
TL;DR: Similarity solutions for a moving wedge and flat plate in a micropolar fluid may be obtained when the fluid and boundary velocities are proportional to the same power-law of the downstream coordinate.
86 citations
TL;DR: In this paper, an implicit method is developed for solving the complete 3D Navier-Stokes equations, based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid.
Abstract: An implicit method is developed for solving the complete three-dimensional (3D) Navier–Stokes equations. The algorithm is based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid. A new top-layer pressure treatment and a partial cell bottom treatment are introduced so that the 3D model is fully non-hydrostatic and is free of any hydrostatic assumption. A domain decomposition method is used to segregate the resulting 3D matrix system into a series of two-dimensional vertical plane problems, for each of which a block tri-diagonal system can be directly solved for the unknown horizontal velocity. Numerical tests including linear standing waves, nonlinear sloshing motions, and progressive wave interactions with uneven bottoms are performed. It is found that the model is capable to simulate accurately a range of free-surface flow problems using a very small number of vertical layers (e.g. two–four layers). The developed model is second-order accuracy in time and space and is unconditionally stable; and it can be effectively used to model 3D surface wave motions. Copyright © 2004 John Wiley & Sons, Ltd.
86 citations
TL;DR: In this article, it was shown that substantial azimuthal current can be driven provided that the amplitude of the rotating magnetic field is greater than a certain threshold value which depends on the plasma resistivity.
Abstract: The generation of a steady azimuthal current in a cylindrical plasma column using a rotating magnetic field is numerically investigated. The mixed initial-boundary-value problem is solved using a finite difference method. It is shown that substantial azimuthal current can be driven provided that the amplitude of the rotating magnetic field is greater than a certain threshold value which depends on the plasma resistivity.
86 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |