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Large-Eddy Simulation (LES) of atmospheric boundary layer (ABL) is an important research method. Until very recently, it was impossible to include detailed surface structures, such as buildings in ABL LES. Nowadays, it is possible to carry out LES e.g. for complex built areas (Letzel et al., 2008). But this is still limited to a relatively small areas because of the high spatial resolution requirement. Xie and Castro (2006) have shown that at least 15 - 20 grid nodes are needed accross street canyons to resolve the most important turbulent structures within the canyons. This typically leads to grid spacings of the order of 1m. However, the extent of the domain should vertically include the whole ABL and the horizontal size should span over several ABL heights. The uncertainty related to the boundary conditions decreases as the domain is made larger. Therefore, even larger domains are highly recommendable.
Many numerical solution methods allow variable resolution so that the resolution can be concentrated to the area of principal interest. However, only unstructured grid systems allow full advantage of variable resolution. Many general-purpose computational fluid dynamics packages offer unstructured grid systems, but such solvers are usually computationally much slower than ABL-tailored LES models, such as PALM (Maronga et al., 2015), that are usually based on structured grid system with constant resolution. Model nesting approach can be exploited to further speed up ABL LES models or to allow larger domain sizes without compromizing the resolution in the area of interest.
The idea of nesting is to simultaneously run a series of two or more LES in model domains with different spatial extents and resolutions. The outermost model is called the root model and it is given boundary conditions on its outer boundaries similarly as in usual LES. The other models are called nest models and their domains are smaller than that of the root and they are nested completely inside the root domain. A nest model can have its own nest models and so on. A nest obtains boundary conditions from its parent. In one-way coupled nesting only the nests obtain information from their parents. However, one-way coupled nesting is known to be of little advantage (Clark and Hall, 1991). In two-way coupled nesting, also the parents are influenced by their nests (Clark and Farley, 1984; Clark and Hall, 1991; Sullivan et al., 1996). The latter interaction may be implemented using e.g. the post insertion (PI) approach (Clark and Hall, 1991) which means that the parent solution is replaced by the restricted nest solution in the domain of overlap. This procedure is called anterpolation. An example of a two-way coupled nesting implemented in the WRF-LES model is given by Moeng et al. (2007). However, the WRF-LES nesting is limited to horizontal directions, i.e. all the domains have equal height.
Numerical methods
In this work two-way coupled nesting is implemented in the parallelized LES model, PALM (Maronga et al., 2015). PALM is based on the non-hydrostatic, filtered, incompressible Navier-Stokes equations together with a subgrid-scale model according to Deardorff (1980). PALM solves the transport equations in staggered Arakawa C grid with horizontally constant grid spacing. The vertical grid spacing may be stretched. The solution method is a projection method in which a provisional velocity field is first integrated from the momentum equations without the pressure gradient term using three-step Runge-Kutta scheme. Then perturbation pressure is solved from a Poisson equation and the provisional velocity is projected to solenoidal field using pressure gradient.
Our nesting approach is a variant of the PI method. In the present implementation, the inter-model communication including interpolations and anterpolations is carried out on each Runge-Kutta substep before the pressure-projection step. Interpolation and anterpolation schemes are trilinear.
Implementation
The nested model system is implemented using two levels of MPI communicators. The inter-model communication is handled by a global communicator using the one-sided communication pattern. The intra-model communication is two-sided and it is handled using a 2-D communicator that has different color for each model. The mapping between each parent and nest model domain decompositions is determined in the initialization phase so that the communication during the time-stepping is straightforward and efficient.
Convective boundary layer without mean wind
The system was tested in a convective boundary layer with zero mean wind. Also in this case, the ground is flat with no obstacles. The horizontal size of the root domain is 10.24 km ×10.24 km, and its height is 1.92 km. The resolution is 20 m in all directions. The nest domain size is 5.12 km ×5.12 km ×0.96 km with 10 m resolution. Constant kinematic heat flux of 0.15 K m s-1 is set on the ground surface and there is a capping inversion starting at height of 1250 m. More detailed description of this case is found in Hellsten and Zilitinkevich (2013). Instantaneous vertical velocity component w in an x,z-plane is shown in Figure 1. The figure shows that the solution is continuos over the nest boundaries. Also vertical profiles are continuous and smooth over the nest top boundary.
Neutral boundary layer over an array of obstacles
The next test case is a neutral boundary layer over a uniform non-staggered array of 14×8 rectangular obstacles mounted on flat ground. The obstacle size is 32 m ×32 m ×24 m and their spacing is 32 m in both directions. The ABL height is about 250 m and the root domain size is 2.048 km ×0.512 km ×0.512 km and resolution is 2 m. The nest domain size is 512 m ×256 m ×128 m and resolution is 1 m. Figure 2 shows that the solution is again continuos over the nest boundaries. Also vertical profiles are continuous and smooth over the nest top boundary.
The next step will be to validate the system against measurement data in a realistic urban ABL test case.
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