论文标题
直接数值模拟和大涡模拟的网格点和时间步长要求
Grid-point and time-step requirements for direct numerical simulation and large-eddy simulation
论文作者
论文摘要
我们重新审视Choi和Moin [Phys的网格点需求估计值。 Fluid，24，011702（2012）]，并为空间发展的湍流边界层建立了直接数值模拟（DNS）和大涡模拟（LES）的更通用的网格点要求。我们表明，通过允许局部网格间距按照本地的kolmogorov长度尺度进行扩展，请求的网格点要求是空间发展的湍流边界层的DNS $ n \ sim re_ {l_x}^{2.05} $ n \ sim re_ sim re_ {l_x} $ a imnoge in coin，in coin in coin and coin，in CON coin和coin点和$ l_x $是板的长度。除了网格点的要求外，我们还估计了DNS和LES的时间步长。 We show that, for a code that treats the convective term explicitly, the time steps required to get converged statistics are $N_t\sim Re_{L_x}/Re_{x_0}^{6/7}$ for wall-modeled LES and $N_t\sim Re_{L_x}/Re_{x_0}^{1/7}$ for wall-resolved LES and DNS（带有不同的预成分），其中$ re_ {x_0} $是入口雷诺数。网格点和时步的需求估计值使我们能够估算DNS和LES的整体成本。根据目前的估计，DNS，壁分辨的LE和壁模型LES比例的成本为$ re_ {l_x}^{2.91} $，$ re_ {l_x}^{2.72} $，和$ re_ re_ re_ re_ re_ {l_x}}^{1.14} $。
We revisit the grid-point requirement estimates in Choi and Moin [Phys. Fluid, 24, 011702 (2012)] and establish more general grid-point requirements for direct numerical simulations (DNS) and large-eddy simulations (LES) of a spatially developing turbulent boundary layer. We show that, by allowing the local grid spacing to scale with the local Kolmogorov length scale, the grid-point requirement for DNS of a spatially developing turbulent boundary layer is $N\sim Re_{L_x}^{2.05}$ rather than $N\sim Re_{L_x}^{2.64}$ as suggested by Choi and Moin, where $N$ is the number of grid points and $L_x$ is the length of the plate. In addition to the grid-point requirement, we estimate the time-step requirement for DNS and LES. We show that, for a code that treats the convective term explicitly, the time steps required to get converged statistics are $N_t\sim Re_{L_x}/Re_{x_0}^{6/7}$ for wall-modeled LES and $N_t\sim Re_{L_x}/Re_{x_0}^{1/7}$ for wall-resolved LES and DNS (with different prefactors), where $Re_{x_0}$ is the inlet Reynolds number. The grid-point and time-step requirement estimates allow us to estimate the overall cost of DNS and LES. According to present estimates, the costs of DNS, wall-resolved LES and wall-modeled LES scale as $Re_{L_x}^{2.91}$, $Re_{L_x}^{2.72}$, and $Re_{L_x}^{1.14}$.
