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Computer Simulation for
Predicting Acoustic Scattering from Objects at the Bottom of the Ocean
Verification & Validation
In the modern world of computational science, computer simulation has evolved to become the third essential re- search methodology, alongside theory and experiment (Oberkampf, 2002; Post, 2005). Since computer simulation is prone to human errors throughout the development and modeling process, it is important, in order to achieve reli- able solutions, to continually subject models to a process of experimental validation (of the physics) and numerical veri- fication (of the mathematics), also known as V&V (Figure 7). Ideally, this is a continuous, never-ending process.
Following are two examples, one of verification and one of validation. Both examples illustrate an essential feature of V&V: a comparison of two different approaches to a prob- lem. Each approach has strengths and weaknesses and is prone to human error, so neither solution is certain. Thus, V&V is a two-way street, each approach providing increased confidence in the other. As more and more V&V testing is done, it might be said that one’s confidence level can ap- proach certainty asymptotically!
Figure 8. Verification of computer simulation of scattering from spherical shell resting on sediment on ocean bottom, vis-à-vis an in- dependent analytical technique (T-matrix method).
Figure 7. Validation of physics and verification of mathematics.
Verification
Verification is often accomplished by comparing two mod- els using independent modeling techniques and looking for agreement over a broad range of the variables (not just at a few isolated spots). The rationale is this: two modeling tech- niques that use different methods are unlikely to produce the same errors over a broad, continuous span of data; ergo, if both solutions agree, then there are probably no errors, so both have probably found the correct solution.
Figure 9. Validation of computer simulation of scattering from a solid aluminum cylinder resting on sediment, vis-à-vis data from an in-water experiment. (Experimental data exhibit noise at the low frequencies due to a low signal-to-noise ratio for the equipment.)
34 | Acoustics Today | Winter 2015