Check accuracy
The aerodynamic modal load matrix Q
is computed using the modal normal loads n_hat
. These loads shall be obtained as follows:
- Obtain the pressure at
t
equidistant time instances (p_i
) - Integrate the pressure on each cell for the
t
time instances (n_i = \int n_i * p_i dA_i
) - Convert the normal load in the frequency domain using the direct fourier transform (
n_hat_i = dft_ij * n_j
) - Retain the second mode (first harmonic,
n_hat_1
)
This method presents a serious drawback: the pressure must first be computed in the time domain. However, the pressure can be directly obtained in the frequency domain. Consequently, the code currently converts the pressure to the frequency domain first, and then integrate the pressure to obtain the loads in the frequency domain. This is mathematically correct only if the geometry on which the integration is performed does not change. However, the geometry does deform with time, so it is important to ensure that the deformation is small. Even so, the accuracy of the results should be checked (i.e. the code should be validated).
If the accuracy of the results cannot be demonstrated, then the data should first be converted to the time domain, processed in the time domain, then converted back to the frequency domain.