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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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
-
Piecewise Polynomial Mapping Method and Corresponding WENO Scheme with Improved Resolution
Li, Qin | Liu, Pengxin | Zhang, HanxinCommunications in Computational Physics, Vol. 18 (2015), Iss. 5 P.1417
https://doi.org/10.4208/cicp.150215.250515a [Citations: 21] -
Analysis of spectral properties of WENO schemes in smooth regions
Wu, Conghai | Luo, Yong | Han, Shuaibin | Li, Hu | Zhang, ShuhaiCommunications in Nonlinear Science and Numerical Simulation, Vol. 130 (2024), Iss. P.107777
https://doi.org/10.1016/j.cnsns.2023.107777 [Citations: 0] -
A Fourth-Order Symmetric WENO Scheme with Improved Performance by New Linear and Nonlinear Optimizations
Li, Qin | Guo, Qilong | Sun, Dong | Liu, Pengxin | Zhang, HanxinJournal of Scientific Computing, Vol. 71 (2017), Iss. 1 P.109
https://doi.org/10.1007/s10915-016-0293-7 [Citations: 9] -
Quasi-linear analysis of dispersion relation preservation for nonlinear schemes
Xu, Fengyuan | Yan, Pan | Li, Qin | You, YanchengAdvances in Aerodynamics, Vol. 4 (2022), Iss. 1
https://doi.org/10.1186/s42774-022-00104-2 [Citations: 1] -
Analysis of Weno Schemes for Local Shapes
Wu, Conghai | Luo, Yong | Han, Shuaibin | Li, Hu | Zhang, ShuhaiSSRN Electronic Journal , Vol. (2022), Iss.
https://doi.org/10.2139/ssrn.4166565 [Citations: 0] -
Nonlinear Upwind-Biased Free-Stream-Preserving Schemes for Compressible Euler Equations
Li, Qin | Sun, Dong | Yan, Pan | Huang, XiaoJournal of Scientific Computing, Vol. 91 (2022), Iss. 3
https://doi.org/10.1007/s10915-022-01833-8 [Citations: 0] -
The enhanced optimized scheme for linear wave propagation
Wu, Conghai | Ma, Ruixuan | Wang, Yimin | Han, Shuaibin | Zhang, ShuhaiJournal of Computational Physics, Vol. 518 (2024), Iss. P.113278
https://doi.org/10.1016/j.jcp.2024.113278 [Citations: 0]