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

Published online by Cambridge University Press:  03 June 2015

Qin Li
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, Sichuan, China National Laboratory of Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Qilong Guo
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, Sichuan, China
Hanxin Zhang
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, Sichuan, China National Laboratory of Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
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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 & Martín’s third-order scheme.

Type
Research Article
Copyright
Copyright © Global-Science Press 2013

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