Study And Applications Of High-order Accurate Dissipative Compact Schemes

Dissipative Compact Scheme(DCS) derived by Deng Xiaogang is a kind of linear high-order accurate scheme(HOS) with single parameter. DCS not only has the characteristics of high resolution, high accuracy and poor demand for grid number, but also owns the particular advantages of depressing the surge of high wave-number. Fifth-order DCS with fourth-order boundary schemes is studied in this thesis, and used to resolve eigenvalue problem of supersonic plane Couette flow and its boundary value stability problem.This thesis is divided into seven chapters, which are resumptively described as follows:The first chapter is the introduction, in which the necessity of developing HOS is described. Then the development of HOS at home and abroad is reviewed also. Finally, the research work of this thesis is described briefly.The second chapter is used to describe the introduction and theoretical analysis of DCS. The detailed methods of constructing DCS is given. Then, Fourier analysis of errors associated with DCS is emphasized, and the asymptotic stabilities of DCS in the uniform grids is also analyzed.In the third chapter, DCS-5 is used in one dimension free-space propagation of simple harmonic wave, to investigate the effects of parameters of scheme and grid point density.In the fourth chapter, DCS-5 is used to resolve eigenvalue problem of supersonic plane Couette flow and its boundary value stability problem, and the results show that this scheme has the advantage of good dispersive characteristics. The concluding remarks are given in the fifth chapter, where the summary of current study work is presented and some work to be carried on in future is pointed out as well.In the end, the references and acknowledgements are presented.