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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.


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Journal ArticleDOI
TL;DR: In this article, the Navier-Stokes equations were approximated to fourth-order accuracy with stencils extending only over a 3 x 3 square of points, and the key advantage of the new compact 4-order scheme is that it allows direct iteration for low-to-mediwn Reynolds numbers.
Abstract: SUMMARY We note in this study that the Navier-Stokes equations, when expressed in streamfunction-vorticity fonn, can be approximated to fourth--order accuracy with stencils extending only over a 3 x 3 square of points. The key advantage of the new compact fourth-order scheme is that it allows direct iteration for low~to-mediwn Reynolds numbers. Numerical solutions are obtained for the model problem of the driven cavity and compared with solutions available in the literature. For Re $1500 point-SOR iteration is used and the convergence is fast.

238 citations

Journal ArticleDOI
TL;DR: A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom, and it is shown to provide convergent solutions over the full physical and discrete parameter space of interest.

238 citations

Journal ArticleDOI
TL;DR: Finite difference and particle tracking methods for solving the tempered fractional diffusion equation with drift are provided and a new exponential rejection method for simulating tempered Levy stables is presented to facilitate particle tracking codes.

235 citations

Journal ArticleDOI
TL;DR: In this article, a method for implementing the general Floquet boundary condition in the finite-difference time-domain algorithm (FDTD) is presented, where the Floquet type of phase shift boundary condition is incorporated into the time domain analysis by illuminating the structure with a combination of sine and cosine excitations to generate a phasor representation at each time step.
Abstract: A method for implementing the general Floquet boundary condition in the finite-difference time-domain algorithm (FDTD) is presented. The Floquet type of phase shift boundary condition is incorporated into the time-domain analysis by illuminating the structure with a combination of sine and cosine excitations to generate a phasor representation of the solution at each time step. With this approach, the characteristics of periodic structures comprised of arbitrarily shaped inhomogeneous geometries can be computed for an arbitrary angle of incidence. Theoretical results are compared for various planar frequency selective surfaces (FSS) and for one with a three-dimensional element, e.g., a thick, double, concentric square loop. >

234 citations

Journal ArticleDOI
TL;DR: In this paper, a formalism for deriving systematically invariant, symmetric finite difference algorithms for nonlinear evolution differential equations that admit conserved quantities is presented in the context of exact finite difference calculus, and results on the nonlinear stability of a class of algorithms that are derived using the proposed formalism, and that preserve energy or linear momentum, are discussed.
Abstract: In a previous work, the authors have presented a formalism for deriving systematically invariant, symmetric finite difference algorithms for nonlinear evolution differential equations that admit conserved quantities. This formalism is herein cast in the context of exact finite difference calculus. The algorithms obtained from the proposed formalism are shown to derive exactly from discrete scalar potential functions using finite difference calculus, in the same sense as that of the corresponding differential equation being derivable from its associated energy function (a conserved quantity). A clear ramification of this result is that the derived algorithms preserve certain discrete invariant quantities, which are the consistent counterpart of the invariant quantities in the continuous case. Results on the nonlinear stability of a class of algorithms that are derived using the proposed formalism, and that preserve energy or linear momentum, are discussed in the context of finite difference calculus. Some ...

233 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023125
2022320
2021724
2020681
2019667
2018694