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 depth-integrated, non-hydrostatic model with a semi-implicit finite difference scheme was proposed to model weakly dispersive wave propagation, transformation, breaking, and run-up.
Abstract: This paper describes the formulation, verification, and validation of a depth-integrated, non-hydrostatic model with a semi-implicit, finite difference scheme. The formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. A momentum-conserved advection scheme enables modeling of breaking waves without the aid of analytical solutions for bore approximation or empirical equations for energy dissipation. An upwind scheme extrapolates the free-surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This greatly improves the model stability, which is essential for computation of energetic breaking waves and run-up. The computed results show very good agreement with laboratory data for wave propagation, transformation, breaking, and run-up. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non-hydrostatic solution is directly applicable to existing nonlinear shallow-water models. Copyright © 2008 John Wiley & Sons, Ltd.
303 citations
TL;DR: In this paper, a framework for modeling coupled nucleation, growth and coarsening in diluted alloys is presented, based on the method of finite differences, where the particle distribution is divided into a series of discrete size classes, each represented by a control volume.
301 citations
TL;DR: In this article, an efficient numerical method for solving the fractional diffusion equation (FDE) is considered based upon Chebyshev approximations, which reduces FDE to a system of ordinary differential equations, which is solved by the finite difference method.
298 citations
TL;DR: This work constructs a stable high-order finite difference scheme for the compressible Navier-Stokes equations, that satisfy an energy estimate, and shows the theoretical third-, fourth-, and fifth-order convergence rate, for a viscous shock, where the analytic solution is known.
298 citations
TL;DR: In this paper, Chen et al. developed an unstructured grid, finite volume, three-dimensional (3D) primitive equation coastal ocean model (FVCOM) for the study of coastal ocean and estuarine circulation.
Abstract: [1] An unstructured grid, finite volume, three-dimensional (3-D) primitive equation coastal ocean model (FVCOM) has been developed for the study of coastal ocean and estuarine circulation by Chen et al. (2003a). The finite volume method used in this model combines the advantage of finite element methods for geometric flexibility and finite difference methods for simple discrete computation. Currents, temperature, and salinity are computed using an integral form of the equations, which provides a better representation of the conservative laws for mass, momentum, and heat. Detailed comparisons are presented here of FVCOM simulations with analytical solutions and numerical simulations made with two popular finite difference models (the Princeton Ocean Model and Estuarine and Coastal Ocean Model (ECOM-si)) for the following idealized cases: wind-induced long-surface gravity waves in a circular lake, tidal resonance in rectangular and sector channels, freshwater discharge onto the continental shelf with curved and straight coastlines, and the thermal bottom boundary layer over the slope with steep bottom topography. With a better fit to the curvature of the coastline using unstructured nonoverlapping triangle grid cells, FVCOM provides improved numerical accuracy and correctly captures the physics of tide-, wind-, and buoyancy-induced waves and flows in the coastal ocean. This model is suitable for applications to estuaries, continental shelves, and regional basins that feature complex coastlines and bathymetry.
297 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |