Simulation of all-scale atmospheric dynamics on unstructured meshes

Abstract

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudoincompressible systems, common in large-eddy simulation of small-and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weatherprediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed.

Non-oscillatory forward-in-time integrators for viscous incompressible flows past a sphere

“…The proven implicit largeeddy simulation (ILES) capability of the MPDATA has been particularly enabling for these advancements; cf. [58] for a recent review. Yet, because ILES fundamentally relies on dissipative properties of the leading truncation terms of non-oscillatory advection, it lacks the implicit filtering action in a no-flow direction, and especially in the direction normal to an impermeable boundary.…”

“…Finite-volume discretisations on hybrid meshes combining prismatic elements near solid boundaries and tetrahedra elements elsewhere have become increasingly popular in simulations of viscous engineering flows [22]. In contrast, although unstructured meshes have been a subject of meteorological interest for some time-see [58] for an extended overview-their intrinsic flexibility, have been put to practical use only at the beginning of the present century, in the context of forecasting high-impact weather, air quality and environmental hazard [2]. Since then, there has been a continuously growing research into modelling atmospheric flows on unstructured meshes.…”

“…Apart from the MPDATA's sign-preservation property-one of the primary requirements of atmospheric modelling-the algorithm also provides inherent ability to control numerical oscillations resulting, e.g., from discontinuous representation of shock waves in compressible flows [53] or use of non-staggered meshes for incompressible flows. In the implementations presented here all dependent flow variables are collocated, to lower memory and communication requirements compared to staggered arrangements as well as to facilitate the design of elaborate semi-implicit time integrations schemes [57,58,24,59]. For incompressible engineering flows and anelastic atmospheric flows, instabilities arise with the collocated variables from the coupling between velocity and pressure.…”

On the Interpretation of Gravity Wave Measurements by Ground-Based Lidars

“…The flow solver has been applied to a wider range of scales simulating various problems, like boundary layer flow through complex geometries [41,42], baroclinic instability [43], gravity waves [44][45][46] or even solar convection [47]. Recently, the solver has been advanced to unstructured meshes; see [48].…”

A Class of Finite-Volume Models for Atmospheric Flows Across Scales

“…A study demonstrating the applicability and flexibility of the finite volume discretisation operating on unstructured meshes for the NFT class of atmospheric nonhydrostatic models shows that the approach can complement established, semi-implicit semi-Lagrangian NWP methods. A record of consistent and accurate simulations using the advocated approach keeps growing [11,12] and provides the evidence that the approach has the potential to efficiently resolve a broad range of atmospheric motions, from planetary down to convection where non-hydrostatic effects dominate. Further technical challenges of time to solution and energy efficiency are currently being addressed within Energy-efficient Scalable Algorithms for weather Prediction at Exascale (ESCAPE) programme of research.…”