隐式大涡模拟中二维太阳对流的数值收敛
Numerical convergence of 2D solar convection in implicit large-eddy simulations
摘要：
大涡模拟（LES）和隐式LES（ILES）是对高雷诺数（Re）下湍流不可行的直接数值模拟（DNS）的明智且经济的替代方案。然而，对于观测约束很少的系统，确定这些策略是否充分捕获系统的物理特性是一个艰巨的挑战。在这里，我们解决这个问题，通过分析在二维湍流对流的ILES的数值收敛，与$64^2$和$2048^2$网格点之间的分辨率，随着其有效粘度的估计，导致$1$和$\sim10^4$之间的有效雷诺数。我们的模型的热力学结构类似于太阳内部，包括一小部分的辐射区和对流区。在对流层中，ILES解收敛的模拟与$\ge 512^2$网格点，证明了流动的积分性质和它的功率谱。最重要的是，我们发现，即使是$128^2$网格点的分辨率，Re $\sim10$，是足以捕捉大尺度的动态准确。这是ILES方法的结果，允许这些尺度中包含的能量在低分辨率和高分辨率的模拟中是相同的。需要特别注意的是，在一个小的密度尺度的高度驱动的精细结构的形成未解决的数值网格的区域。在稳定层中，我们发现了内部重力波的激发，但需要高分辨率来捕捉它们的发展和相互作用。
英文摘要：
Large-eddy simulations (LES) and implicit LES (ILES) are wise and affordable alternatives to the unfeasible direct numerical simulations (DNS) of turbulent flows at high Reynolds numbers (Re). However, for systems with few observational constraints, it is a formidable challenge to determine if these strategies adequately capture the physics of the system. Here we address this problem by analyzing numerical convergence of ILES of turbulent convection in 2D, with resolutions between $64^2$ and $2048^2$ grid points, along with the estimation of their effective viscosities, resulting in effective Reynolds numbers between $1$ and $\sim10^4$. The thermodynamic structure of our model resembles the solar interior, including a fraction of the radiative zone and the convection zone. In the convective layer, the ILES solutions converge for the simulations with $\ge 512^2$ grid points, as evidenced by the integral properties of the flow and its power spectra. Most importantly, we found that even a resolution of $128^2$ grid points, Re$\sim10$, is sufficient to capture the dynamics of the large scales accurately. This is a consequence of the ILES method allowing that the energy contained in these scales is the same in simulations with low and high resolution. Special attention is needed in regions with a small density scale height driving the formation of fine structures unresolved by the numerical grid. In the stable layer we found the excitation of internal gravity waves, yet high resolution is needed to capture their development and interaction.
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