Reduced aliasing formulations of the convective terms within the Navier-Stokes equations for a compressible fluid
Reduced aliasing formulations of the convective terms within the Navier-Stokes equations for a compressible fluid
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DOI：
10.1016/j.jcp.2007.09.020
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
C. Kennedy;A. Gruber
中科院分区：
文献类型：
--
作者：
C. Kennedy;A. Gruber
在非平凡的密度谱的存在下，研究了离散化Navier-Stokes方程中描述立方非线性对流项的不同配方对混叠误差的影响。傅立叶分析表明，现有的反对称形式的对流项的结果在减少混淆错误相对于守恒形式。几个配方的对流项，包括一个新的配方提出的立方非线性项，在衰减的可压缩各向同性湍流在化学惰性（小密度波动）和反应的情况下（大密度波动）和不同程度的分辨率直接数值模拟（DNS）进行测试。在反应湍流的DNS中，新的立方斜对称形式给出了最准确的结果，与谱误差分析一致，并且成本最低。在边缘解决DNS和LES（解决不好的定义）的新的立方反对对称形式代表了一个强大的对流配方，最大限度地减少混叠和计算成本，同时也允许减少使用计算昂贵的高阶耗散滤波器。
The effect on aliasing errors of different formulations describing the cubically nonlinear convective terms within the discretized Navier–Stokes equations is examined in the presence of a non-trivial density spectrum. Fourier analysis shows that the existing skew-symmetric forms of the convective term result in reduced aliasing errors relative to the conservation form. Several formulations of the convective term, including a new formulation proposed for cubically nonlinear terms, are tested in direct numerical simulation (DNS) of decaying compressible isotropic turbulence both in chemically inert (small density fluctuations) and reactive cases (large density fluctuations) and for different degrees of resolution. In the DNS of reactive turbulent flow, the new cubic skew-symmetric form gives the most accurate results, consistent with the spectral error analysis, and at the lowest cost. In marginally resolved DNS and LES (poorly resolved by definition) the new cubic skew-symmetric form represents a robust convective formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high-order dissipative filters.