# Extrapolation tool comparison to full model not agree in waveform shape Answered

I made a small model (2" x 4") axial symmetric model with a pressure source. I ran the model and recorded the acoustic pressure 3" from the pressure source and also set up an extrapolation output about 10 mesh elements from the pressure source. I used the extrapolation tool to compute the acoustic pressure 3" from the pressure source and compared it to that recorded from the full model in both the time and frequency domains. In the time domain, the results have similar PTP amplitudes but completely different shapes. In the frequency domain, the magnitude of the frequency responses compare well. Is the differences in the time domain expected or does it indicate that I don't have the problem set up correctly?

## 3 comments

Tapiwa MutasaThe time domain signals should be similar, so this is not expected. I suspect that the full model suffered from numerical dispersion. This is something that happens with fea but is exacerbated by long propagation paths and inadequate meshing.

Numerical dispersion will not be discernible in the magnitude frequency profile but will be discernible in the time domain signal or the phase.

For models that are 10s of wavelength long, we usually recommend a meshing of 15 elements per wavelength to minimize dispersion error. For larger models you can mitigate against this, by using a finer mesh along with a timestep factor that is closer to 1. Mesh convergence studies can help determine whether you have sufficient meshing.

In general, extrapolation will give a more accurate result for larger propagation distances in infinite media.

Straub, Chip [EMR/MSOL/HSTN]I tried again with after increasing the mesh from 20 elements/wavelength to 100 elements/wavelength. Comparison of the time domain results between the full model and extrapolated results are much better.

The extrapolated results did appear to be inverted. Is this inversion of the extrapolate results expected?

Tapiwa MutasaThe results should not be inverted. Can you check that you are referencing the same data for your comparison. Acoustic pressure is a different from standard pressure being negated by convention. Extrapolation outputs, on the other hand are standard pressure. This might be the source of the difference.

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