Evaluating numerical methods by using asymptotic limit solutions
Seminar Room 1, Newton Institute
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.