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Evaluating numerical methods by using asymptotic limit solutions

Presented by: 
Mike Cullen Met Office
Date: 
Thursday 27th September 2012 - 10:15 to 10:40
Venue: 
INI Seminar Room 1
Session Title: 
Tests Cases
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.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons