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Here we developed a lattice Boltzmann model on a 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions.
Surface rainfall estimates from radar, traditionally derived at scales of order 1 km, are now requested at grid lengths of 100 m to drive improvements in the outputs of these models.
The scheme is derived as a weighted average of the conventional, forward-in-time, explicit diffusion scheme over one grid length and the same scheme, but over two grid lengths.
The grid lengths Δx and Δz are constrained to Δx=Δz=0.1227c/ω pe.
Calculated density contrast model beneath Aso volcano in horizontal slices at depths of 3.1, 4.9, and 8.2 km: (a), (b), and (c) use mean grid lengths of 500 , 750 and 1000 m, respectively (Additional file 5: Table S3).
Density contrasts tested include variations of ±0.15, ±0.20, ±0.25, ±0.35, and ±0.40 g/cm3 (Additional file 2: Figure S2; Additional file 4: Table S1); homogeneity parameters tested include 0.4, 0.6, and 0.8 (Additional file 3: Figure S3; Additional file 5: Table S2); and mean grid lengths tested include 750 and 1000 m (Additional file 4: Figure S4; Additional file 5: Table S3).
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The model equation utilizes the turbulent length scale, the Kolmogorov length scale and the cut-off grid length.
The two dimensional space is covered by a grid with a grid length given by Δs.
Furthermore, Nigeria requires an average of 0.43 m of MV grid length and 25.01 m of LV grid length to connect various households in each LGA that are grid compatible.
For instance, assume Beijing has an area of S (nearly to 16,800 km2), the grid count is equal to S/l 2 where l is the grid length.
Variations in parameters are tested one by one, based on the basic model (i.e., ±0.3 g/cm3, homogeneity parameter 0.2, and mean grid length 500 m).
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