Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme

Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme

Year:    2013

Author:    Qin Li, Qilong Guo, Hanxin Zhang

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 6 : pp. 809–824

Abstract

Analyses were performed on the dispersion overshoot and inverse dissipation of the high-order finite difference scheme using Fourier and precision analysis. Schemes under discussion included the pointwise- and staggered-grid type, and were presented in weighted form using candidate schemes with third-order accuracy and three-point stencil. All of these were commonly used in the construction of difference schemes. Criteria for the dispersion overshoot were presented and their critical states were discussed. Two kinds of instabilities were studied due to inverse dissipation, especially those that occur at lower wave numbers. Criteria for the occurrence were presented and the relationship of the two instabilities was discussed. Comparisons were made between the analytical results and the dispersion/dissipation relations by Fourier transformation of typical schemes. As an example, an application of the criteria was given for the remedy of inverse dissipation in Weirs and Martin's third-order scheme.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2012.m5

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 6 : pp. 809–824

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    High-order difference scheme dispersion overshoot inverse dissipation.

Author Details

Qin Li

Qilong Guo

Hanxin Zhang