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Characteristic-based flux partitioning for atmospheric flows and a posteriori error estimation

Banff International Research Station for Mathematical Innovation and Discovery

I will discuss two topics: characteristic-based flux partitioning and a posteriori error estimation. In the first part I introduce a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows and discuss it in the context of compressible Euler equations. Here the acoustic time-scale is significantly faster than the advective scale, yet it is typically not relevant to atmospheric and weather phenomena. The acoustic and advective components of the hyperbolic flux are separated in the characteristic space. Results with high-order, conservative additive Runge-Kutta methods are briefly discussed. In the second part I will briefly discuss some new time-stepping strategies with built-in global error estimators. These methods can be cast as general linear schemes that provide pointwise a posteriori errors. I will show some preliminary results on ODE and PDE problems.

Mathematics; Numerical analysis; Partial differential equations; Scientific computing

video/mp4

Author affiliation: Argonne National Laboratory

2019-06-03

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/70454

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/