High-order accurate dissipative weighted compact nonlinear schemes

被引：5
作者：
Xiaogang Deng
机构：
[1] China Aerodynamics Research and Development Center,
来源：
Science in China Series A: Mathematics | 2002年 / 45卷 / 3期
关键词：
numerical calculation; compact schemes; nonlinear schemes; Euler equations; Navier-Stokes equations;
D O I：
10.1360/02ys9037
中图分类号：
学科分类号：
摘要：
Based on the method deriving dissipative compact linear schemes ( DCS), novel high-order dissipative weighted compact nonlinear schemes (DWCNS) are developed. By Fourier analysis, the dissipative and dispersive features of DWCNS are discussed. In view of the modified wave number, the DWCNS are equivalent to the fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the accuracy of DWCNS. Boundary and near boundary schemes are developed and the asymptotic stabilities of DWCNS on both uniform and stretching grids are analyzed. The multi-dimensional implementations for Euler and Navier-Stokes equations are discussed. Several numerical inviscid and viscous results are given which show the good performances of the DWCNS for discontinuities capturing, high accuracy for boundary layer resolutions, good convergent rates (the root-mean-square of residuals approaching machine zero for solutions with strong shocks) and especially the damping effect on the spurious oscillations which were found in the solutions obtained by TVD and ENO schemes.
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页码：356 / 370
页数：14
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