高精度非线性格式WCNS的分析研究与其应用  

Study of high-order accurate weighted compact nonlinear schemes and applications to multi-dimensional viscous flow

作　　者：刘昕[1] 邓小刚[1] 毛枚良[1] 

机构地区：[1]中国空气动力研究与发展中心,四川绵阳621000

出　　处：《计算力学学报》2007年第3期264-268,共5页Chinese Journal of Computational Mechanics

基　　金：国家杰出青年科学资助基金(10225208);创新研究群体科学资助基金(10321002)资助项目

摘　　要：首先将Fourier方法推广于高维方向研究了五阶精度WCNS的特性,并与其他高阶格式进行比较。分析结果表明WCNS的高精度特性普遍接近甚至好于迎风偏置五阶显式格式EUW-5与Pade′标准格式。然后开展了WCNS的应用研究,采用高效率的WCNS-E-5数值模拟了含强激波的高维复杂流场。算例包括二维高超声速边界层对自由流扰动波的吸收问题以及三维球头绕流问题。计算结果反映出WCNS-E-5对激波等间断的良好捕捉能力,图像清晰光滑,数据准确可靠。The theoretical analysis of weighted compact nonlinear schemes （WCNS） and applications to multi-dimensional complicated viscous flows are described in this paper. At first, features of fifth-order WCNS （including WCNS-5 and WCNS-E-5） and other high-order accurate schemes （HOS） such as explicit upwind biased fifth-order scheme （EUW-5） and standard Pade scheme are analyzed with Fourier method. The analytical results show that WCNS have better characteristics than EUW-5 in terms of dispersive and dissipative errors. They also have the higher resolving efficiency than EUW-5 and Pade＇ scheme. The anisotropic errors of these HOS are different little among one another, and they are altogether limited to a narrow range of short waves. Subsequently the high efficient scheme of WCNS-E-5 is used to simulate several complicated flows containing strong shock waves. The tests include two-dimensional hypersonic boundary layer receptivity over parabola and three-dimensional flow past sphere. The numerical solutions show that WCNS-E-5 owns the advantage of capturing shock waves robustly. There are clear and smooth contours without nonphysical oscillations, and the data are correct and reliable.

关 键 词：高精度格式 加权紧致非线性格式 FOURIER分析 波吸收现象 粘性流动 

分 类 号：O354.4[理学—流体力学]