Documentation

The mesh for a Pedestrian Wind Comfort analysis (PWC) is quite different than for the Finite-Volume-based fluid dynamics analysis types on SimScale, as it is based on the lattice-Boltzmann method (LBM). Here a cartesian background mesh is generated, which is composed only of cube elements that are not necessarily aligned with the geometry of the buildings or the terrain.

To take into account the exact geometry, there exists a sub-grid model that accounts for the interfaces between the geometry and the fluid domains.

The big advantage of the lattice-Boltzmann method is that the grid size is not bound by the small details of the geometry and that it is a lot more robust with respect to inaccuracies in the CAD model such as small holes, overlaps, or intersections.

The sizing for the background mesh for the PWC analysis is highly automated and targeted towards the specific use case, thus it works best for model sizes of 1 – 10 \(km^2\) and a region of interest radius of 200 \(m\) – 500 \(m\).

Note

If you are specifically looking for mesh guidelines for the **City of London**, they can be found here.

The main logic of the mesh algorithm is as follows:

- The finest cells are located near the surfaces of the geometry. In the region of interest, there is a two-level finer minimum cell size used than outside of it.
- Close to the surface there will be a layer of 4-6 cells of the smallest cell size.
- Away from the surfaces, roughly every 4 cells, there is an increase in cell size by a factor of 2 where again 4 cells of constant size are added.
- Additional refinements are added in the leeward side of the buildings (there we have roughly 16 cells of the same size) in order to accurately resolve the wake region. This refinement is adapted for each wind direction individually in accordance with the actual wind direction.
- The value of the maximum and minimum cell size used depends on the fineness level and the radius of the region of interest. In general, the smaller the region of interest, the smaller the minimum cell size. Details can be deduced from the table below (Table 1):

Fineness | Number of Refinements Levels | Number of Cells per Disc Diameter |
---|---|---|

Very Coarse | 4 | 16 |

Coarse | 5 | 16 |

Moderate | 5 | 24 |

Fine | 6 | 16 |

Very Fine | 6 | 24 |

$$ Maximum\ Cell\ Size = \frac{ Disc\ Diameter}{Number\ of\ Cells\ Per\ Disc\ Diameter} $$

$$ Minimum\ Cell\ Size = \frac{ Maximum\ Cell\ Size}{2^{Number\ of\ Refinement\ Levels}} $$

The following example (Table 2) shows maximum and minimum cell sizes per disc radius, using automatic meshing process.

ROI Radius \([m]\) | Very Coarse max / min \([m]\) | Coarse max / min \([m]\) | Moderate max / min \([m]\) | Fine max / min \([m]\) | Very Fine max / min \([m]\) |
---|---|---|---|---|---|

100 | 12.5 / 0.8 | 12.5 / 0.4 | 8.3 / 0.3 | 12.5 / 0.2 | 8.3 / 0.1 |

200 | 25.0 / 1.6 | 25.0 / 0.8 | 16.7 / 0.5 | 25.0 / 0.4 | 16.7 / 0.3 |

300 | 37.5 / 2.3 | 37.5 / 1.2 | 25.0 / 0.8 | 37.5 / 0.6 | 25.0 / 0.4 |

400 | 50 / 3.1 | 50.0 / 1.6 | 33.3 / 1.0 | 50.0 / 0.8 | 33.3 / 0.5 |

Based on the desired fineness level one can approximate the mesh size as follows (Table 3):

Fineness | Very Coarse | Coarse | Moderate | Fine | Very Fine |
---|---|---|---|---|---|

Relative minimum size | 1 | 1/2 | 1/3 | 1/4 | 1/6 |

Minimum size per 100 \(m\) radius | 0.78 | 0.39 | 0.26 | 0.20 | 0.13 |

Relative cell count approximation | 1 | 2 | 4 | 8 | 16 |

- If explicitly a minimum cell size target is needed, this can also be defined using the
*Target size*option. This makes sure that the minimum cell size in the region of interest is at most as large as the target cell size (it can be lower). The exact value is reported in the run info. This option is specifically useful if one wants to make sure to meet the cell size requirements that certain wind standards (such as*London Wind Microclimate Guidelines*or the Dutch*NEN8100 Wind Standard*) require.

- The actual cell count depends on multiple factors, such as the diameter of the (ROI) region of interest \((D)\), the height of the buildings \((h)\), the size of the wind tunnel and the complexity of the CAD model. A rough estimation for cell count for different diameter to height ratios can be seen below (Table 4), assuming a
*Large*wind tunnel is selected from the*Region of interest*>*Advanced settings*and a relatively simple CAD model:

Ratio \(D/h\) | Very Coarse | Coarse | Moderate | Fine | Very Fine |

\(D/h\) = 2 | 10e6 | 12e6 | 25e6 | 45e6 | 100e6 |

\(D/h\) = 4 | 4e6 | 5e6 | 12e6 | 18e6 | 45e6 |

\(D/h\) = 10 | 1.5e6 | 3e6 | 7e6 | 10e6 | 20e6 |

The Reynolds scaling factor can be accessed under *Mesh settings*. The Reynolds number is defined as \(Re= \frac{UL}/{\nu} \) where \(L\) is the reference length, \(U\) is the velocity, and \(\nu \) is the kinematic viscosity of the fluid. When a scaling factor is applied, instead of sizing the geometry down, the viscosity is increased to ensure that the Reynolds number is reduced to the correct scaling.

In most urban scale flows, an ** Automatic Reynolds scaling is recommended** to ensure accurate results. Like wind tunnel models, we use Reynolds scaling assuming that bluff bodies (block-like buildings) and high Reynolds numbers are present. This enables the concept of similarity of large Reynolds numbers. When both these conditions are met, automatic scaling is valid. Automatic Reynolds scaling helps you get accurate results, cheaper without extensive expertise.

Advanced users operating outside the typical assumptions of urban scales are welcome to use manual scaling, however, they should consider the impacts on wall modeling and rely on their expertise. A scale of 1 represents full scale, and 1/250 or 1/400 would represent a typical wind tunnel scale. Automatic values in SimScale are typically in the order of 1/10.

Sometimes it is required to put additional focus on specific regions like entrance areas, narrow street canyons between high rise buildings, complex terrain or vegetation, and local mesh refinements in these regions are desired.

In such cases, either a *Surface refinement* or a *Region refinement *can be added.

A surface refinement is best suited for cases where a specific building or a set of its surfaces or solids should be refined.

The fineness can be defined analogously to the global mesh sizing from *Very coarse* to *Very fine*. Also, in the same way, as it is done for the global mesh sizing inside the region of interest, the surface refinement will result in a layer of 4-6 cells of the smallest cell size and gradually increasing with a larger distance from the surface.

In case a region between two buildings or a specific open area that is of interest would need to be refined, a region refinement would be best suited. In order to locate the region where the mesh should be refined, a *geometry primitive* of type *sphere* or *box* can be created using the **‘+’ **button and assigned by activating the slider in front of it.

The sizing for the region of interest is the same as for the global sizing and the surface refinement, but in contrast to them, the smallest cell size will be kept throughout the whole assigned domain.

Note

As a general recommendation, a local refinement that is more than one level finer than the global fineness is to be avoided as it will reduce the overall simulation efficiency. In such cases it is rather recommended to also reduce the global mesh size and limit the size difference to one level.

References

Last updated: August 21st, 2023

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