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For verification purposes, we may want to compute the Nusselt number, which indicates whether heat transport is due to conduction or convection.
A standard test in RBC is to compute the Nusselt number averaged over the entire volume and over the top and bottom plates. Conservation of energy than requires the time average over the three to match.
Doing this test is expensive, though, because time averaging requires sufficiently long simulation time.

The PR includes tests that the Nusselt numbers get the expected values for a bunch of situations. Also, I added a test for integration in ultraspherical base with non-standard domain size.

@pancetta pancetta merged commit b460650 into Parallel-in-Time:master Jul 30, 2025
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@brownbaerchen brownbaerchen deleted the nusselt branch August 5, 2025 14:37
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2 participants