Search

In large-eddy simulations (LES) a computational-domain translation velocity can be used to improve performance by allowing longer time-step intervals. The continuous equations are Galilean invariant, however, standard finite-difference-based discretizations are not discretely invariant with the error being proportional to the product of the local translation velocity and the truncation error. Even though such numerical errors are expected to be small, it is shown that in LES of buoyant convection the turbulent large-scale flow organization can modulate and amplify the error. Galilean invariance of global flow statistics is observed in well-resolved direct numerical simulations (DNS). In LES of single-phase convection under an inversion, flow statistics are nearly Galilean invariant and do not depend on the order of accuracy of the finite difference approximation. In contrast, in LES of cloudy convection, flow statistics show strong dependence on the frame of reference and the order of approximation. The error with respect to the frame of reference becomes negligible as the order of accuracy is increased from second to sixth in the present LES. Schemes with low resolving power can produce large dispersion errors in the surface-fixed frame that can be amplified by large-scale flow anisotropies, such as strong updrafts rising in a non-turbulent free troposphere in cumulus-cloud layers. Interestingly, in the present large-eddy simulations, a second-order discretization in the proper Galilean frame can yield comparable accuracy as a high-order scheme in the surface-fixed frame., Comment: arXiv admin note: substantial text overlap with arXiv:1907.05554

A computational domain translation velocity is often used in LES simulations to improve computational performance by allowing longer time-step intervals. Even though the equations of motion are Galilean invariant, LES results have been observed to depend on the translation velocity. It is found that LES results of shallow convection depend on the domain translation velocity even when a Galilean invariant formulation is used. This type of model error is named residual cross-grid flow error, to emphasize the expectation that it should be negligible or zero. The residual gross-grid flow error is caused by biases in finite difference dispersion errors. Schemes with low resolving power (typically low order of accuracy) produce larger dispersion errors that can be amplified by large-scale flow asymmetries, such as strong updrafts in cumulus-cloud layers. Accordingly, the cross-grid flow error strongly depends on the order of accuracy of the numerical scheme progressively becoming negligible as the order of accuracy is increased from second to sixth in the present simulations., Comment: 17 pages, 11 figures

This short article describes flow parameters, numerical method, and animations of the fluid dynamics video "LES of an Inclined Jet into a Supersonic Turbulent Crossflow" (http://ecommons.library.cornell.edu/bitstream/1813/14073/3/GFM-2009.mpg [high-resolution] and http://ecommons.library.cornell.edu/bitstream/1813/14073/2/GFM-2009-web.m1v [low-resolution] video). We performed large-eddy simulation with the sub-grid scale (LES-SGS) stretched-vortex model of momentum and scalar transport to study the gas-dynamics interactions of a helium inclined round jet into a supersonic ($M=3.6$) turbulent (\Reth$ =13\times10^3$) air flow over a flat surface. The video shows the temporal development of Mach-number and magnitude of density-gradient in the mid-span plane, and isosurface of helium mass-fraction and $\lam_2$ (vortical structures). The identified vortical structures are sheets, tilted tubes, and discontinuous rings. The vortical structures are shown to be well correlated in space and time with helium mass-fraction isosurface ($Y_{\rm He}=0.25$)., Comment: 7 pages, 1 figure, 1 table, article describing fluid dynamics video submitted to Gallery of Fluid Motion, APS-DFD 2009

This short article describes flow parameters, numerical method, and animations of the fluid dynamics video LES of an Inclined Jet into a Supersonic Cross-Flow (http://hdl.handle.net/1813/11480). Helium is injected through an inclined round jet into a supersonic air flow at Mach 3.6. The video shows 2D contours of Mach number and magnitude of density gradient, and 3D iso-surfaces of Helium mass-fraction and vortical structures. Large eddy simulation with the sub-grid scale (LES-SGS) stretched vortex model of turbulent and scalar transport captures the main flow features: bow shock, Mach disk, shear layers, counter-rotating vortices, and large-scale structures., Comment: Video contribution to Gallery of Fluid Motion 2008 (APS-DFD)

computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts