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Highly oscillatory PDEs, slow manifolds and regularized PDE formations

Reich, S (Potsdam)
Tuesday 27 March 2007, 11:30-12:15

Seminar Room 1, Newton Institute


The main motivation of my talk is provided by geophysical fluid dynamics. The underlying Euler or Navier-Stokes equations display oscillatory wave dynamics on a wide range of temporal and spatial scales. Simplified models are often based on the idea of balance and the concept of a slow manifold. Examples are provided by hydrostatic and geostrophic balance. One would also like to exploit these concepts on a computational level. However, slow manifolds are idealized objects that do not fully characterize the complex fluid behavior. I will describe a novel regularization technique that makes use of balance and slow manifolds in an adaptive manner. The regularization approach is based on a reinterpretation of the (linearly) implicit midpoint rule as an explicit time-stepping method applied to a regularized set of Euler equations. Adaptivity can be achieved by means of a predictor-corrector interpretation of the regularization.




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