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Evaluating numerical methods by using asymptotic limit solutions

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Multiscale Numerics for the Atmosphere and Ocean

Numerical models of the atmosphere and ocean ‘solve’ the governing Navier-Stokes equations, but because of the complexity of the true solutions, can only do so in a grossly averaged sense. Standard numerical analysis theory is then of limited use, because it expects solutions to be close to the truth. The Navier-Stokes equations are known to have solutions close to computable asymptotic limits in many cases of practical interest. This talk gives examples, including dynamics/boundary-layer interaction, frontal solutions where the asymptotic limit is singular, and long-term behaviour of baroclinic systems, together with numerical demonstrations. The technique should help to validate the new integration schemes being proposed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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