### Evaluating numerical methods by using asymptotic limit solutions

**Mike Cullen, ***(Met Office)*

Thursday 27 September 2012, 10:15-10:40

Seminar Room 1, Newton Institute

#### Abstract

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.

#### Presentation

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