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On Subgrid Models and Filter Operations in Large Eddy Simulations

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  • 1 Meteorological Office, Bracknell, Berkshire, United Kingdom
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Abstract

Large eddy simulations use a subgrid model, which is characterized by a length scale that is often related to the scale of the computational mesh by a numerical constant, Cs. Mason and Callen argued that this subgrid model and its length scale define and impose the filter operation of the simulation. They saw Cs as a measure of numerical accuracy. Others have sought to link the filter operation to the computational mesh and have viewed Cs as needing determination for correct implementation. Here tests with a high resolution of 224 × 224 × 200 grid points are found to confirm Mason and Callen’s view. These simulations are also used together with lower-resolution simulations to illustrate the degree of convergence achieved. Some erroneous features of the simulations are identified through this test.

For the case of buoyant convection, the buoyancy dependence of the subgrid model is further examined. Most available subgrid models allow for buoyancy fluxes changing the level of the subgrid energy but only allow stable buoyancy gradients to modify the subgrid length scale—a reduction in this case. In contrast to most applications, it has been suggested that for a fixed filter operation, the subgrid length scale should always have a buoyancy dependence and should increase, in a finite way, with unstable buoyant transfer. Here an examination of spectral behavior in high-resolution simulations supports such an approach and shows that the model with the buoyancy-dependent length scale is indeed consistent with a fixed filter operation. The more conventional models are shown to have less satisfactory behavior.

Corresponding author address: Dr. Andrew R. Brown, Meteorological Office, Bracknell, Berkshire RG12 2SZ, United Kingdom.

Email: arbrown@meto.gov.uk

Abstract

Large eddy simulations use a subgrid model, which is characterized by a length scale that is often related to the scale of the computational mesh by a numerical constant, Cs. Mason and Callen argued that this subgrid model and its length scale define and impose the filter operation of the simulation. They saw Cs as a measure of numerical accuracy. Others have sought to link the filter operation to the computational mesh and have viewed Cs as needing determination for correct implementation. Here tests with a high resolution of 224 × 224 × 200 grid points are found to confirm Mason and Callen’s view. These simulations are also used together with lower-resolution simulations to illustrate the degree of convergence achieved. Some erroneous features of the simulations are identified through this test.

For the case of buoyant convection, the buoyancy dependence of the subgrid model is further examined. Most available subgrid models allow for buoyancy fluxes changing the level of the subgrid energy but only allow stable buoyancy gradients to modify the subgrid length scale—a reduction in this case. In contrast to most applications, it has been suggested that for a fixed filter operation, the subgrid length scale should always have a buoyancy dependence and should increase, in a finite way, with unstable buoyant transfer. Here an examination of spectral behavior in high-resolution simulations supports such an approach and shows that the model with the buoyancy-dependent length scale is indeed consistent with a fixed filter operation. The more conventional models are shown to have less satisfactory behavior.

Corresponding author address: Dr. Andrew R. Brown, Meteorological Office, Bracknell, Berkshire RG12 2SZ, United Kingdom.

Email: arbrown@meto.gov.uk

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