arXiv 1805.034262018-05-09physics.flu-dynphysics.comp-ph

有源或无源标量turbulence有限体积程序的多分辨格式

Multiple-resolution scheme in finite-volume code for active or passive scalar turbulence

Kai Leong Chong, Guangyu Ding, Ke-Qing Xia

备注：: 16 pages, 11 figures, submitted to Journal of Computational Physics
DOI：: 10.1016/j.jcp.2018.09.019

摘要：

在标量湍流中，有时候标量扩散系数小于粘性扩散系数。水中的热驱动湍流对流就是一个典型的例子。在这种情况下，问题中的最小标度是巴彻勒标度$l_b$，而不是柯尔莫哥洛夫标度$l_k$，如$l_b = l_k/Sc^{1/2}$，其中Sc是施密特数（或温度情况下的普朗特数）。在对这种标量湍流的数值研究中，传统的方法是对速度场和标量场采用单一网格。由于$l_b<l_k$对$Sc>1$的分辨率要求比速度场高，因此这种单分辨率格式往往过分辨速度场。在本文中，我们提出了一种算法，实现了所谓的多分辨率方法与有限体积的代码。在该格式中，速度场和压力场在粗网格中求解，而标量场在密网格中求解。其核心思想是在有限体积框架下实现插值格式，从粗网格到密网格重建无发散速度。我们证明了我们的方法使用一个典型的模型系统的流体湍流，瑞利-贝纳德对流。我们表明，与定制的网格设计，可以实现相当大的加速模拟标量湍流，特别是对于大施密特（普朗特）数。同时，该多分辨率格式可以保证标量场和速度场的足够精度。虽然我们的算法是用一个主动标量的情况下，它可以很容易地应用到被动标量湍流。

英文摘要：

In scalar turbulence it is sometimes the case that the scalar diffusivity is smaller than the viscous diffusivity. The thermally-driven turbulent convection in water is a typical example. In such a case the smallest scale in the problem is the Batchelor scale $l_b$, rather than the Kolmogorov scale $l_k$, as $l_b = l_k/Sc^{1/2}$, where Sc is the Schmidt number (or Prandtl number in the case of temperature). In the numerical studies of such scalar turbulence, the conventional approach is to use a single grid for both the velocity and scalar fields. Such single-resolution scheme often over-resolves the velocity field because the resolution requirement for scalar is higher than that for the velocity field, since $l_b<l_k$ for $Sc>1$. In this paper we put forward an algorithm that implements the so-called multiple-resolution method with a finite-volume code. In this scheme, the velocity and pressure fields are solved in a coarse grid, while the scalar field is solved in a dense grid. The central idea is to implement the interpolation scheme on the framework of finite-volume to reconstruct the divergence-free velocity from the coarse to the dense grid. We demonstrate our method using a canonical model system of fluid turbulence, the Rayleigh-Bénard convection. We show that, with the tailored mesh design, considerable speed-up for simulating scalar turbulence can be achieved, especially for large Schmidt (Prandtl) numbers. In the same time, sufficient accuracy of the scalar and velocity fields can be achived by this multiple-resolution scheme. Although our algorithm is demonstrated with a case of an active scalar, it can be readily applied to passive scalar turbulent flows.

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摘要：

英文摘要：

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