Wind loads simulation convergence

Wind simulation does not result in totally stable results as it is a dynamic process changing over time.

In order to address this problem, the program measures the resulting total forces convergence over a specific time period.

Total Forces

The resultant forces are monitored in three directions:

• In the direction of the wind: .
• Horizontally and perpendicularly to the wind direction: .
• In the vertical direction: .

Scaling Forces

The resultant forces depend on the model size. To properly scale the resultant forces, the program uses the dynamic pressure and the surface values ,, and .

The surface values are used to scale the corresponding forces.

This approach allows for the neutralization of disproportions of the model in the wind directions x, y and z.

These relative values are calculated as follows:

• 
  Where:

  • represents the dynamic pressure in pascals.
  • represents the fluid density in kg/m³ .
  • represents the fluid velocity in m/s.
• The surface corresponds to the area covered by the projection of all the triangles of the model on the plane perpendicular to the X wind direction.
• The surface corresponds to the area covered by the projection of all the triangles of the model on the plane perpendicular to the Y wind direction.
• The surface corresponds to the area covered by the projection of all the triangles of the model on the plane perpendicular to the Z wind direction.

The scaling forces are calculated as follows:

Assessment of resultant forces stabilization

To measure the total forces convergence over a specific time period, the resultant forces , , and are calculated and stored for a number of steps n, and then the maximum change for a given moment is calculated as follows:

Where , , and represent the stored values of , , and for a given step, and for i=1 to n.

These maximum force changes are then scaled by , , and respectively and displayed as a percentage.

The final metric is the maximum of these three scaled values:

Where = 0,5%, i.e. the default load deviation factor.

Note: In order for the metric to be fully valid, at least n steps of the simulation must be performed.

n is the number of simulation steps for which , , and are stored for comparison with the current step. The default value for n is 10.