| 19 | |
| 20 | == Topography parameterization == |
| 21 | The Cartesian topography in PALM is generally based on the mask method ([#briscolini1989 Briscolini and Santangelo, 1989]) and allows for explicitly resolving solid obstacles such as buildings and orography. The implementation makes use of the following simplifications: |
| 22 | |
| 23 | 1. the obstacle shape is approximated by (an appropriate number of) full grid cells to fit the grid, i.e., a grid cell is either 100% fluid or 100% obstacle, |
| 24 | |
| 25 | 2. the obstacles are fixed (not moving). |
| 26 | |
| 27 | Topography is realized in 3-D, e.g., overhanging structures as for example bridges, ceilings, or tunnels, are allowed, i.e. topography does not necessarily be surface-mounted. If no overhanging structures are present, the 3-D obstacle dimension reduces to a 2.5-D topography format, which is conform to the Digital Elevation Model (DEM) format (DEMs of city morphologies have become increasingly available worldwide due to advances in remote sensing technologies). |
| 28 | In case of overhanging structures, however, 3-D topography information is required to mask obstacles and their faces in PALM. |
| 29 | |
| 30 | The model domain is then separated into three subdomains: |
| 31 | |
| 32 | A. grid points in free fluid without adjacent surfaces, where the standard PALM code is executed, |
| 33 | |
| 34 | B. grid points next to surface that require extra code (e.g., surface parametrization), and |
| 35 | |
| 36 | C. grid points within obstacles, where the standard PALM code is executed but multiplied by zero. |
| 37 | |
| 38 | Additional topography code is executed in grid volumes of subdomain B. The faces of the obstacles are always located where the |
| 39 | respective surface-normal velocity components ''u'', ''v'', and ''w'' are defined so that the impermeability boundary condition can be implemented by setting the respective surface-normal velocity component to zero. |
| 40 | |
| 41 | In case of 5th-order advection scheme, the numerical stencil at grid points adjacent to obstacles would require data which is located within the obstacle. |
| 42 | In order to avoid this, the order of the advection scheme is successively degraded at respective grid volumes adjacent to obstacles, i.e., from the 5th-order to 3rd-order at the second grid point above/beside an obstacle and from 3rd-order to 1st-order at grid points directly adjacent to an obstacle. |
| 43 | |
| 44 | Simulations with topography require the application of MOST between each surface and the first computational grid point outside of the topography. |
| 45 | For vertical and horizontal downward-facing surfaces, neutral stratification is assumed for MOST. |
| 46 | |
| 47 | In the PALM core, buildings are primarily realized as obstacles that react to the flow dynamics via form drag |
| 48 | and friction forces by assuming a constant flux layer between the building surface and the adjacent air volume. A simple thermodynamic coupling is also possible by prescribing surface fluxes of sensible (and latent heat) at any of the building surface grid elements. |
| 49 | |
| 50 | The technical realization of the topography and treatment of surface-bounded grid cells is be outlined in Section [wiki:doc/tec/topography topography implementation]. |