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
1 / 2
Papers
TL;DR: A robust and efficient algorithm in which the mesh equations are uncoupled from the physical PDE is demonstrated, and a novel automatic time-step control mechanism is integrated into the scheme.
88 citations
TL;DR: In this paper, an up-wind finite-volume algorithm for accurate numerical simulation of incompressible flows and convection heat transfer on unstructured grids is presented, where flow variables are calculated along characteristics and their initial values are interpolated based on the signs of corresponding characteristic speed.
88 citations
1 Jul 1993
TL;DR: The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations and an application to flow around an airfoil is presented.
Abstract: The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations are considered. The relation between them for both the continuous problem and the finite difference approximation is also considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Hence, the steady state of the preconditioned system is the same as the steady state of the original system. For finite difference methods the preconditioning can change and improve the steady state solutions. An application to flow around an airfoil is presented.
88 citations
TL;DR: In this paper, a particle-based model for the simulation of wave propagation is presented, which is based on solid-state physics principles and considers a piece of rock to be a Hookean material composed of discrete particles representing fundamental intact rock units.
Abstract: Summary
A particle-based model for the simulation of wave propagation is presented. The model is based on solid-state physics principles and considers a piece of rock to be a Hookean material composed of discrete particles representing fundamental intact rock units. These particles interact at their contact points and experience reversible elastic forces proportional to their displacement from equilibrium. Particles are followed through space by numerically solving their equations of motion. We demonstrate that a numerical implementation of this scheme is capable of modelling the propagation of elastic waves through heterogeneous isotropic media. The results obtained are compared with a high-order finite difference solution to the wave equation. The method is found to be accurate, and thus offers an alternative to traditional continuum-based wave simulators.
88 citations
TL;DR: A ‘modified equation’ analysis is used to characterize grid-dependent anisotropies in the discretization and motivates a new family of finite difference schemes that show essentially no dependence on the orientation of the grid.
87 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |