Compact finite difference schemes on non-uniform meshes. Application to direct numerical simulations of compressible flows
Compact finite difference schemes on non-uniform meshes. Application to direct numerical simulations of compressible flows
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DOI：
10.1002/(sici)1097-0363(19990130)29:2
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发表时间：
1999-01
影响因子：
1.8
通讯作者：
L. Gamet;F. Ducros;F. Nicoud;T. Poinsot
中科院分区：
文献类型：
--
作者：
L. Gamet;F. Ducros;F. Nicoud;T. Poinsot
在本文中，研究了用于逼近非均匀网格上的一阶（分别是二阶）导数的四阶（分别是三阶）紧凑方案的开发。提出了将度量完全包含在紧凑方案的系数中，而不是使用雅可比变换的方法。第二部分对数值方案进行了分析。提出了截断误差的数值分析，以及通过半离散和全离散特征值问题的稳定性计算完成的傅里叶分析。在这些特征值问题中，考虑一阶导数的纯对流方程和二阶导数的纯扩散方程。本文的最后一部分致力于数值方法在需要可变网格尺寸的可压缩流模拟中的应用：可压缩湍流通道流的直接数值模拟。目前的结果与文献中的实验数据和其他数值 (DNS) 数据进行了比较。讨论了压缩性和声波对湍流结构的影响。
In this paper, the development of a fourth- (respectively third-) order compact scheme for the approximation of first (respectively second) derivatives on non-uniform meshes is studied. A full inclusion of metrics in the coefficients of the compact scheme is proposed, instead of methods using Jacobian transformation. In the second part, an analysis of the numerical scheme is presented. A numerical analysis of truncation errors, a Fourier analysis completed by stability calculations in terms of both semi- and fully discrete eigenvalue problems are presented. In those eigenvalue problems, the pure convection equation for the first derivative, and the pure diffusion equation for the second derivative are considered. The last part of this paper is dedicated to an application of the numerical method to the simulation of a compressible flow requiring variable mesh size: the direct numerical simulation of compressible turbulent channel flow. Present results are compared with both experimental and other numerical (DNS) data in the literature. The effects of compressibility and acoustic waves on the turbulent flow structure are discussed.