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Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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TL;DR: In this paper, the finite difference procedure and the subgrid scale (SGS) motion model are used to simulate high Reynolds number turbulent flows of incompressible fluids in plane channels and annuli, and the boundary conditions are formulated in a manner consistent with the SGS theory.
1,386 citations
Book•
27 Sep 1996
TL;DR: In this paper, the authors define and define nonlinear hyperbolic systems in one space dimension and define finite difference schemes for one-dimensional systems in the case of multidimensional systems.
Abstract: From the contents: Introduction: Definitions and Examples.- Nonlinear hyperbolic systems in one space dimension.- Gas dynamics and reaction flows.- Finite Difference Schemes for one-dimensional systems.- The case of multidimensional systems.- An Introduction to Boundary conditions.
1,386 citations
TL;DR: In this paper, the authors developed methods where by the differential equations of physics may be applied more freely than hitherto in the approximate form of difference equations to problems concerning irregular bodies, and all that was there said, as to the need for new methods, may be taken to apply here also.
Abstract: 1. Introduction.— 1·0. The object of this paper is to develop methods where by the differential equations of physics may be applied more freely than hitherto in the approximate form of difference equations to problems concerning irregular bodies. Though very different in method, it is in purpose a continuation of a former paper by the author, on a “Freehand Graphic Way of Determining Stream Lines and Equipotentials” (‘Phil. Mag.,’February, 1908; also ‘Proc. Physical Soc.,’ London, vol. xxi.). And all that was there said, as to the need for new methods, may be taken to apply here also. In brief, analytical methods are the foundation of the whole subject, and in practice they are the most accurate when they will work, but in the integration of partial equations, with reference to irregular-shaped boundaries, their field of application is very limited.
1,364 citations
TL;DR: In this paper, the authors developed practical numerical methods to solve one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain and demonstrated the practical application of these results is illustrated by modeling a radial flow problem.
1,334 citations
TL;DR: In this article, it was shown that the derived form of the finite difference Jacobian can prevent nonlinear computational instability and thereby permit long-term numerical integrations, which is not the case in finite difference analogues of the equation of motion for two-dimensional incompressible flow.
1,328 citations