Optimized finite-difference (DRP) schemes perform poorly for decaying or growing oscillations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:324

Article

Brambley, E. J.¹ 

[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Wilberforce Rd, Cambridge CB3 0WA, England

关键词: Optimized finite differences;    Computational aeroacoustics;    DRP schemes;    Damped waves;   

DOI  :  10.1016/j.jcp.2016.08.003

来源: Elsevier

【 摘 要 】

Computational aeroacoustics often use finite difference schemes optimized to require relatively few points per wavelength; such optimized schemes are often called Dispersion Relation Preserving (DRP). Similar techniques are also used outside aeroacoustics. Here the question is posed: what is the equivalent of points per wavelength for growing or decaying waves, and how well are such waves resolved numerically? Such non-constant-amplitude waves are common in aeroacoustics, such as the exponential decay caused by acoustic linings, the O(1/r) decay of an expanding spherical wave, and the decay of high-azimuthal-order modes in the radial direction towards the centre of a cylindrical duct. It is shown that optimized spatial derivatives perform poorly for waves that are not of constant amplitude, under performing maximal-order schemes. An equivalent criterion to points per wavelength is proposed for non-constant-amplitude oscillations, reducing to the standard definition for constant-amplitude oscillations and valid even for pure growth or decay with no oscillation. Using this definition, coherent statements about points per wavelength necessary for a given accuracy can be made for maximal-order schemes applied to non-constant-amplitude oscillations. These features are illustrated through a numerical example of a one-dimensional wave propagating through a damping region. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free