Semi-implicit finite-volume integrators for all-scale atmospheric dynamics

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Advanced Numerical Methods for Scientific Computing
Piotr Smolarkiewicz
European Centre for Medium-Range Weather Forecasts, Reading, Berkshire, United Kingdom
Thursday 30th May 2019
Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO
This talk outlines a novel numerical approach for accurate and computationally efficient integrations of PDEs governing all-scale atmospheric dynamics. Such PDEs are not easy to handle, due to a huge disparity of spatial and temporal scales as well as a wide range of propagation speeds of natural phenomena captured by the equations. Moreover, atmospheric dynamics constitutes only a small perturbation about dominant balances that result from the Earth gravity, rotation, composition of its atmosphere and the energy input by the solar radiation. Maintaining this mean equilibrium, while accurately resolving the perturbations, conditions the design of atmospheric models and subjects their numerical procedures to stringent stability, accuracy and efficiency requirements. The novel Finite-Volume Module of the Integrated Forecasting System (IFS) at ECMWF (hereafter IFS-FVM) solves perturbation forms of the fully compressible Euler/Navier-Stokes equations under gravity and rotation using non-oscillatory forward-in-time semi-implicit time stepping and finite-volume spatial discretisation. The IFS-FVM complements the established semi-implicit semi-Lagrangian pseudo-spectral IFS (IFS-ST) with the all-scale deep-atmosphere formulation cast in a generalised height-based vertical coordinate, fully conservative and monotone advection, flexible horizontal meshing and a predominantly local communication footprint. Yet, both dynamical cores can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude-latitude coordinates and physics parametrisations, thus facilitating their synergetic relation. The focus of the talk is on the mathematical/numerical formulation of the IFS-FVM with the emphasis on the design of semi-implicit integrators and the associated elliptic Helmholtz problem. Relevant benchmark results and comparisons with corresponding IFS-ST results attest that IFS-FVM offers highly competitive solution quality and computational performance. Contact:
Piotr Smolarkiewicz received M.Sc. and Ph.D. degrees from the University of Warsaw, in geophysics and physical sciences in 1973 and 1980, respectively. In 1981, he went to Boulder, Colorado, to join as a post-doctoral fellow in the Advanced Study Program at the National Center for Atmospheric Research (NCAR). Since 1973, he has been an assistant professor at the Department of Physics, University of Warsaw. After the post-doctoral appointment, since 1983 he has been a scientist at NCAR, in the rank of Senior Scientist since 1994. In 2005-2006, he served as an NCAR Science Advisor, and since 2007 he has been the Head of the Computational Mathematics Group at the Institute for Mathematics Applied to Geosciences (IMAGe) of NCAR. In 2013 he joined the Research Department of the European Centre for Medium-Range Weather Forecasts (ECMWF) as a consultant. Piotr's research centres on computational fluid dynamics (CFD), with particular emphasis on all-scale geophysical circulations and basic fluid dynamic of rotating stratified flows. He is the principal developer of the multi-scale, multi-physics, high-performance research code EULAG built on high-resolution transport methods MPDATA, which he has originated and developed at NCAR. Piotr’s interests include scientific computing, geophysical flows of all scales, solar dynamo, physics of plasmas, non-Newtonian fluids, and dynamics of continuous media. His current activities at ECMWF focus on the development of an interdisciplinary forecasting system (PantaRhei) for simulating multi-scale fluid flows.