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.