J4.3 Large-eddy Simulation across a Grid Refinement Interface Using Explicit Filtering and Reconstruction

Large-eddy simulation (LES) is commonly used in atmospheric simulations when the domain size is small enough to allow grid spacing that resolves turbulence. At these resolutions LES is more accurate than the Reynolds-averaged Navier-Stokes (RANS) models used for mesoscale simulations, but far less computationally intensive than direct numerical simulation (DNS). Grid nesting, used to transfer the meso-scale boundary conditions to a micro-scale domain of interest, is another popular technique. The use of LES on nested grids, while common in micro-scale atmospheric simulations, presents challenges not encountered in RANS or DNS simulations. On a two-way nested grid, the solution must be approximated across the grid refinement interface to calculate derivatives at the interface. This approximation necessarily uses information at the grid scale, i.e. the solution points directly surrounding the interpolated point. Interpolation is not problematic in DNS or RANS codes, because the solutions resulting from these methods are smooth at all scales. Neither DNS nor RANS solutions contain substantial energy at the grid scale, so the grid scale is not particularly inaccurate. However, LES solutions are least accurate at the grid scale, because the grid scale is most heavily contaminated by the subgrid scale (SGS) stress approximation, as shown in Brandt (2006). Interpolation therefore introduces errors on both sides of the interface between grids of different refinements. LES solutions can also reflect off grid refinement interfaces, specifically on the outflow boundary from a fine to a coarse grid. A coherent structure that is resolvable on a fine grid but not a coarse grid may interact with a fine to coarse interface several ways. The eddy may alias onto the coarse grid, represented as a motion with a larger wavelength, it may dissipate, or it may reflect. Reflection creates the more problematic errors, since the reflection appears as an accumulation of energy on the fine side of a grid refinement interface. In grid nesting applications, modelers often want to develop smaller scales of turbulence as quickly as possible from the coarse to the fine grid. The solution immediately inside the fine, interior grid has less re-