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

作　　者：Qin Li Qilong Guo Hanxin Zhang 

机构地区：[1]State Key Laboratory of Aerodynamics,Mianyang 621000,Sichuan,China [2]National Laboratory of Computational Fluid Dynamics,Beijing University of Aeronautics and Astronautics,Beijing 100191,China

出　　处：《Advances in Applied Mathematics and Mechanics》2013年第6期809-824,共16页应用数学与力学进展（英文）

基　　金：This work was sponsored by the National Science Foundation of China under Grant number 10972023 and 11272037;also partially supported by National Basic Research Program of China(No.2009CB724100).The first author was very grateful to Prof.Frank Lu for his efforts on the revision of the manuscript.

摘　　要：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&Mart´ın’s third-order scheme.

关 键 词：High-order difference scheme dispersion overshoot inverse dissipation 

分 类 号：O17[理学—数学]