Convecting reference frames and invariant numerical models

JOURNAL OF COMPUTATIONAL PHYSICS

卷:272

Article

Bihlo, Alexander^1,2  Nave, Jean-Christophe² 

[1] Univ Montreal, Ctr Rech Math, Succ Ctr Ville, Montreal, PQ H3C 3J7, Canada

[2] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2KG, Canada

关键词: Geometric numerical integration;    Lie symmetries;    Invariant discretization schemes;    Burgers equation;   

DOI  :  10.1016/j.jcp.2014.04.042

来源: Elsevier

【 摘 要 】

In the recent paper by Bernardini et al. [1] the discrepancy in the performance of finite difference and spectral models for simulations of flows with a preferential direction of propagation was studied. In a simplified investigation carried out using the viscous Burgers equation the authors attributed the poorer numerical results of finite difference models to a violation of Galilean invariance in the discretization and propose to carry out the computations in a reference frame moving with the bulk velocity of the flow. Here we further discuss this problem and relate it to known results on invariant discretization schemes. Non-invariant and invariant finite difference discretizations of Burgers equation are proposed and compared with the discretization using the remedy proposed by Bernardini et al. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free