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Flow-induced Coordinates for Transient Advection-Diffusion Equations with Multiple Scales

Presented by: 
Konrad Simon Universität Hamburg
Tuesday 12th September 2017 - 15:30 to 16:00
INI Seminar Room 1
Co-author: Jörn Behrens (University of Hamburg, Germany)

Simulation over a long time scale in climate sciences as done, e.g., in paleo climate simulations require coarse grids due to computational constraints. Unresolved scales, however, significantly influence the coarse grid variables. Such processes include (slowly) moving land-sea interfaces or ice shields as well as flow over urbanic areas. Neglecting these scales amounts to unreliable simulation results. State-of-the-art dynamical cores represent the influence of subscale processes typically via subscale parametrizations and often employ heuristic coupling of scales.

Our aim is to improve the mathematical consistency of the upscaling process that transfers information from the subgrid to the coarse prognostic scale (and vice-versa). We investigate a new bottom-up techniques for advection dominated problems arising in climate simulations [Lauritzen et al. (2011)]. Our tools are based on ideas for multiscale finite element methods for elliptic problems that play a role in oil reservoir modeling and porous media in general [Efendiev and Hou (2009), Graham et al. (2012)]. Modifying these ideas is in necessary in order to account for the transient and advection dominated character which is typical for flows encountered in climate models.

We present a new Garlerkin based idea to account for the typical difficulties in climate simulations. Our modified ideas employ a change of coordinates based on a coarse grid characteristic transform induced by the advection term in order to account for appropriate subgrid boundary conditions for the multiscale basis functions which are essential for such approaches. We present results from sample runs for a simple advection-diffusion equation with rapidly varying coefficients on several scales.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons