The effect of sub-tree forest heterogeneity in the flow past a clearing is investigated by means of large-eddy simulation (LES). For this purpose, a detailed representation of the canopy has been acquired by terrestrial laser scanning for a patch of approximately 190 m length in the field site "Tharandter Wald", near the city of Dresden, Germany. The scanning data are used to produce a high resolution plant area distribution (PAD) that is averaged over approximately one tree height (30 m) along the transverse direction, in order to simplify the LES study. Despite the smoothing involved with this procedure, the resulting two-dimensional PAD maintains a rich vertical and horizontal structure. For the LES study, the PAD is embedded in a larger domain covered with an idealized, horizontally homogeneous canopy. Simulations are performed for neutral conditions and compared to a LES with homogeneous PAD and recent field measurements. The results reveal a considerable influence of small-scale plant distribution on the mean velocity field as well as on turbulence data. Particularly near the edges of the clearing, where canopy structure is highly variable, usage of a realistic PAD appears to be crucial for capturing the local flow structure. Inside the forest, local variations in plant density induce a complex pattern of upward and downward motions, which remain visible in the mean flow and make it difficult to identify the "adjustment zone" behind the windward edge of the clearing.

Summary A morphology adaptive modeling framework is derived that is able to handle computationally efficiently dispersed as well as resolved interfacial structures coexisting in the computational domain with the same set of equations. The Eulerian multifield two‐fluid model is combined with the compact momentum interpolation method for multiple phases, which has been proposed in the literature as an extension to the Rhie‐Chow pressure‐velocity coupling. Additionally to the interfacial drag force, the virtual mass force is consistently accounted for in the model. Utilizing a specialized interfacial drag formulation, large interfacial structures can be described with the presented method in a volume‐of‐fluid‐like manner, additionally to the disperse description. The strong phase coupling due to the drag closure model in interfacial regions is resolved with a partial elimination algorithm, which is adapted to work in an approximate manner for more than two phases via a sum formulation. The presented model is implemented in the C++ library OpenFOAM and solver performance is compared with results obtained with the homogeneous model approach in two cases of a single rising gas bubble for two‐ and three‐dimensional space, respectively. Additionally, for both three‐dimensional cases, the results are compared with experimental data. Finally, the presented method's capability of representing dispersed and resolved interfacial structures at the same time is demonstrated with two test cases: a two‐dimensional gas bubble, rising in a liquid, which is laden with micro gas bubbles, and a two‐dimensional stagnant stratification of water and oil, sharing a large‐scale interface, which is penetrated by micro gas bubbles.

Summary The numerical solution of the population balance equation is frequently achieved by means of discretization, ie, by the method of classes. An important concern of discrete formulations is the preservation of 2 chosen moments of the distribution, eg, numbers and mass, while remaining flexible on the grid and kernels applied. Existing formulations for breakage are either able to perserve only one moment or restricted by the choice of grid and kernels. Two types of kernel functions for the description of breakup rate exist, ie, total breakup model and partial breakup model. The first type states the total breakup rate of a mother particle and requires a daughter size distribution function. The other type gives the breakup rate between a mother and a daughter particle directly. Existing formulations are known to work well for the former type but inefficiently for the latter one due to the need of additional numerical integrations. The particular focus of the present work lies in developing an efficient formulation for this type of kernels. A discrete formulation of the breakup terms due to binary breakage is proposed, which allows a direct implementation of both types of breakup kernels and an efficient solution of the population balance equation, making it favorable for the coupling to computational fluid dynamics codes. The results for a pure breakage process obtained by using the new formulation and various kernels are compared with those by a reference formulation as well as analytical solutions. Good agreement is achieved in all test cases, and numerical efficiency of the new formulation for partial breakup models is evidenced.

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