Craig J. Tremback and Robert L. Walko Mission Research Corporation

1. Direct Simulation of Flow around Buildings using an Atmospheric Model:New Capabilities for the Regional Atmospheric Modeling System (RAMS) Craig J. Tremback and Robert L. Walko Mission Research Corporation

2. Problems with Terrain-Following () Coordinate Systems • All terrain-following coordinate models have difficulty in handling “steep” topography • In z systems, dependent on ratio ztopo/z • Problems arise in taking horizontal gradients • ETA coordinate model (Mesinger/Janjic) developed to address this problem for p coordinate systems • In z systems, what we really want is a true Cartesian horizontal gradient, but…

3. Terrain-Following Horizontal Gradient Computation

4. The Main Culprit… Horizontal Diffusion • Horizontal diffusion was causing the majority of the “bad” effects in RAMS when topography became too steep. • New method: interpolate model fields from the zlevels to true Cartesian surface, then take gradient. • Allowable Δz improved by a factor of 3-5 in most cases. Disadvantages: • About 15% slower than standard diffusion. There are coding strategies to fix this… • Problems due to horizontal gradients also enter through advection and pressure gradient terms. • Not flux conservative • The lower boundary condition is problematic.

5. A Permanent Solution ? • ETA-type step-coordinate model used successfully: • Simple Cartesian grid easy to implement • Eliminates all coordinate-induced, numerical truncation errors • Runs faster per gridpoint, about 2x faster for basic numerics • Allows arbitrarily steep topography (cliffs, buildings, etc. • However…

6. ETA Disadvantages • However, ETA-type model has drawbacks: • Topography must jump in steps of Δz, even along smooth slopes. • Need to numerically deal with “corners”. W. Gallus showed ETA model generates noise. • Usually needs more gridpoints (and memory/disk), hence slower physics • Gridpoints underground can be blocked from computation relatively easily; not as easy to block from memory (could use “less-structured” grid)

7. ETA Disadvantages • Important drawback to ETA-type coordinate: • Computational issues when desiring high vertical resolution all along a slope 2000 m 0 m

8. Toward a Better Solution… • ADAP (ADaptive APerature) coordinate • Mostly following work of Adcroft, et al for oceanographic model • “Shaved” ETA-type coordinate Standard ETA coordinate ADAP coordinate

9. ADAP Features • Grid structure is a true Cartesian grid. • The apertures of the grid cell faces are adapted to topography that would block the flow. • Implemented as an option in RAMS; z still supported because high-resolution slopes is still an issue. Vertically- nested grids can help… • Same technique can be applied to other types of obstacles: buildings, vegetative canopy, etc. • Allows very complex shapes (overhangs, tunnels, etc.) • All components (topography, buildings, vegetation, etc.) can be present in simulation at same time.

10. RAMS Vertical Nesting • Can add vertically-nested grid along slope • Nest can have same horizontal resolution as “coarse” grid • Nest is not required to extend to model top • Not ideal solution, but can help… 2000 m 0 m

11. ADAP and Vegetation

12. RAMS/ADAP Modifications for Very High-Resolution Simulations • Two-way nested grid communication allows building interaction with “real” weather • Isotropic turbulence options: • Deardorff TKE available for a long time, used in LES runs • Recently implemented E- and E-l (S. Trini Castelli, CNR, Torino, Italy) • All model terms must account for partially-closed apertures • Complete transition of RAMS from finite-difference model to finite-volume model

13. Finite-difference form Finite-difference flux form Finite-volume flux form ADAP Numerical Differencing for Advective Terms

14. RAMS/ADAP Very High-Resolution Simulation Examples • Flow around a single rectangular building • (CEDVAL A1-1, Re = 32750) • Flow through an array of buildings • (CEDVAL B1-1, Re = 56390) • Flow through an array of buildings on a slope • RAMS configuration • Two grids: x = 10 m & 2 m; z = 2 m, stretched • Neutral, horizontally homogeneous initialization • 5 m/s initial flow; Re  100 • Deardorff isotropic TKE subgrid scheme

15. Flow around a single building Building size: x=20m y=30m z=25m Cedval: 1:200

16. Flow around a single building Z = 0.28H

17. Flow through an array of buildings Z = 1 m

18. Flow through an array of buildings

19. Flow through buildings on a slope 5 m/s

20. Flow through buildings on a slope

21. RAMS/ADAP Summary • We have implemented the ADAP coordinate as an alternative to the z coordinate in RAMS. • An important advantage: “Real” weather can interact with buildings through two-way nesting algorithms. • Still has disadvantage of ETA-type coordinate in situations where high vertical resolution along a slope is desired. RAMS vertically-nested grids can help. • Simulations show good qualitative agreement with wind tunnel measurements • Things to do: • Drag on vertical walls • Investigate other physical processes, e.g. radiation (overhangs, shading) • Further investigation of differencing at convex corners • Quantitative validation