Volume 5, Issue 6
Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme

Qin Li, Qilong Guo & Hanxin Zhang

Adv. Appl. Math. Mech., 5 (2013), pp. 809-824.

Published online: 2013-05

Preview Full PDF 51 782
Export citation
  • 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.

  • Keywords

High-order difference scheme dispersion overshoot inverse dissipation

  • AMS Subject Headings

76M20 74P99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-5-809, author = {Qin Li, Qilong Guo and Hanxin Zhang}, title = {Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2012.m5}, url = {http://global-sci.org/intro/article_detail/aamm/97.html} }
TY - JOUR T1 - Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme AU - Qin Li, Qilong Guo & Hanxin Zhang JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 809 EP - 824 PY - 2013 DA - 2013/05 SN - 5 DO - http://dor.org/10.4208/aamm.2012.m5 UR - https://global-sci.org/intro/aamm/97.html KW - High-order difference scheme KW - dispersion overshoot KW - inverse dissipation AB -

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.

Qin Li, Qilong Guo & Hanxin Zhang. (1970). Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme. Advances in Applied Mathematics and Mechanics. 5 (6). 809-824. doi:10.4208/aamm.2012.m5
Copy to clipboard
The citation has been copied to your clipboard