Structural stability of finite dispersion-relation preserving schemes
نویسندگان
چکیده
منابع مشابه
Structural stability of finite dispersion-relation preserving schemes
The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurance of such a spurious solitary wave, which exhibits a very long life time, results in a nonvanis...
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A class of higher-order compact upwind biased finite difference (FD) schemes based on the Taylor Series Expansion is developed in this work. The numerical accuracy of this family of compact upwind biased FD schemes is demonstrated by means of Fourier analysis wherein it is shown that these FD schemes have very low dispersion errors over a relatively large bandwidth of wave numbers as compared t...
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A linear dispersive mechanism leading to a burst in the L∞ norm of the error in numerical simulation of polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity a...
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In developing suitable numerical techniques for computational aero-acoustics, the DispersionRelation-Preserving (DRP) scheme by Tam and coworkers, and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficient...
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The results of a 3D DNS code based on explicit optimized DRP [1] are analyzed for moderate Reynolds number (Re=4200). The aim is to show the ability of these schemes to give accurate results in a small amount of time comparing to others accurate schemes as compact schemes. To this end, we consider a wall-bounded turbulent flow. Periodic boundaries conditions are applied in the streamwise and sp...
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ژورنال
عنوان ژورنال: Chaos, Solitons & Fractals
سال: 2009
ISSN: 0960-0779
DOI: 10.1016/j.chaos.2008.08.028