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
CGG1
TL;DR: In this article, two second-order wave equations for acoustic vertical transversely isotropic (VTI) media are transformed to six first-order coupled partial differential equations for a more straighforward numerical implementation of the derivatives.
Abstract: Two second-order wave equations for acoustic vertical transversely isotropic (VTI) media are transformed to six first-order coupled partial differential equations for a more straighforward numerical implementation of the derivatives. The resulting first-order equations have a more natural form for discretization by any finite-difference, pseudospectral, or finite-element method. I discretized the new equations by high-order finite differences and used synthetic seismograms and snapshots for anisotropic and isotropic cases. The relative merits of placing the source deep and close to a free surface are assessed, illustrating advantages of exciting the source inside or outside of a near-surface, thin, isotropic layer. Results show that traveltimes from deep seismic reflectors can remain virtually unaffected when near-surface isotropic layers are included in acoustic VTI media.
77 citations
TL;DR: In this paper, a methode de calcul des ecoulements stationnaires laminaires a grand nombre de Reynolds is presented, and the equations de Navier-Stokes par differences finies sur une grille en quinconce are discussed.
Abstract: On presente une methode de calcul des ecoulements stationnaires laminaires a grand nombre de Reynolds. Discretisation des equations de Navier-Stokes par differences finies sur une grille en quinconce et utilisation d'une methode de direction alternee implicite
77 citations
TL;DR: This work provides an explicit estimate of the interface misalignment error for the second order in time and space staggered finite-difference scheme applied to the acoustic wave equation and demonstrates that the interface error results in a first-order time shift proportional to the distance between the interface and computational grids.
Abstract: The numerical error associated with finite-difference simulation of wave propagation in discontinuous media consists of two components. The first component is a higher-order error that leads to grid dispersion; it can be controlled by higher-order methods. The second component results from misalignment between numerical grids and material interfaces. We provide an explicit estimate of the interface misalignment error for the second order in time and space staggered finite-difference scheme applied to the acoustic wave equation. Our analysis, confirmed by numerical experiments, demonstrates that the interface error results in a first-order time shift proportional to the distance between the interface and computational grids. A 2D experiment shows that the interface error cannot be suppressed by higher-order methods and indicates that our 1D analysis gives a good prediction about the behavior of the numerical solution in higher dimensions.
77 citations
TL;DR: First- and second-order maximum norm a posteriori error estimates are given that are based on difference derivatives of the numerical solution and hold true uniformly in the small parameter.
Abstract: A singularly perturbed quasi-linear two-point boundary value problem with an exponential boundary layer is discretized on arbitrary nonuniform meshes using first- and second-order difference schemes, including upwind schemes. We give first- and second-order maximum norm a posteriori error estimates that are based on difference derivatives of the numerical solution and hold true uniformly in the small parameter. Numerical experiments support the theoretical results.
77 citations
TL;DR: Comparisons show that the high-order accurate OS schemes may compete well with other numerical schemes discussed here in terms of the accuracy and the efficiency, and the interaction dynamics of two NLD solitary waves depend on the exponent power of the self-interaction in the NLD equation.
77 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |