UC Berkeley

Increasing computational power has enabled grid resolutions that support large-eddy simulation (LES) of the atmospheric boundary layer (ABL). These simulations often use non-uniform block structured grids, particularly nested grids. More complex adaptive mesh refinement (AMR) grids are also used in urban scale simulations. LES and AMR combined can reduce the computational cost of turbulence simulations compared to direct numerical simulation, but the interaction of the smallest resolved scales of the LES solution with grid refinement interfaces can generate additional errors. These errors, such as resolved energy accumulation and spurious numerical forces, may compromise solution accuracy.

In this dissertation, the ability of the LES formulation and turbulence closure model to mitigate these errors is tested. The standard LES equations are compared with explicitly filtered advection (EFA), in which a discrete low-pass filter is applied to the advection term. EFA damps the inaccurate smallest scales of the solution, which contribute most to grid interface error. The turbulence closures tested are static Smagorinsky eddy viscosity and a mixed model including a scale similarity component. The turbulence closure interacts directly with the smallest scales of the solution, so improving the turbulence closure was expected to increase accuracy at these scales. In addition, the mixed model is further improved with active approximate deconvolution to reconstruct the unfiltered velocity field. The explicit filtering operator is also made more continuous by using a variable filter that allowed the filter width to transition continuously between grid sizes.

These techniques are first tested in a simulation of decaying isotropic turbulence advected past a grid refinement interface. Different explicit filter types and levels of reconstruction are tested. Explicit filtering with zero-level reconstruction is found to produce the best long-term convergence to a uniform grid solution with minimum perturbation at the interface. Higher levels of reconstruction yield better near-interface convergence. When explicit filtering is used, the explicit filter width transition is more important than the grid spacing transition in terms of solution convergence and interface perturbation.

Next, a neutral atmospheric boundary layer is simulated by a half-channel approximation. Explicit filtering of the advection term and the mixed model are compared to implicit filtering and the eddy viscosity model. It is found that explicitly filtering the advection term allows both mass and momentum to be conserved across grid refinement interfaces. The mixed model reduces unphysical perturbations generated by wave reflection.

In the last test case, flow through a periodic array of cubes is simulated. This test case is intended to mimic flow through an urban boundary layer. The grid is refined near the cubic obstacles, creating multiple planes of grid refinement interface. Similar errors to those observed in the boundary layer test case were observed, particularly energy accumulation due to wave reflection.

Finally, several details of the implementation of explicitly filtered LES on block-structured non-uniform grids are discussed. Contrary to previous results, commutation errors are not found to be substantial for the decaying isotropic turbulence test case. Use of non-linear interpolation schemes to transfer the solution between grid sizes is found to generate errors in reconstructed velocity values at grid refinement interfaces. When Lagrangian averaging is used in a dynamic eddy viscosity scheme, the averaged quantities are only comparable across a grid refinement interface if variable filtering is used.