Accessibility navigation

Nonlinear diffusion‐limited 2D colliding plume simulations with very high order numerical approximations

Straka, J. M. ORCID:, Williams, P. D. ORCID: and Kanak, K. M. ORCID: (2023) Nonlinear diffusion‐limited 2D colliding plume simulations with very high order numerical approximations. Quarterly Journal of the Royal Meteorological Society. ISSN 1477-870X

[img] Text - Accepted Version
· Restricted to Repository staff only
· The Copyright of this document has not been checked yet. This may affect its availability.


It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1002/qj.4616


Atmospheric numerical models play a crucial role in operational weather forecasting, as well as improving our understanding of atmospheric dynamics via research studies. Maximising their accuracy is of paramount importance. Use of >O7 flux schemes in atmospheric models is largely undocumented, with no studies considering O3–17 fluxes with formal accuracy‐preserving high order interpolation, pressure gradient / divergence, and subgrid‐scale (SGS) turbulent fluxes. Higher order numerical approximations can reduce truncation, amplitude and phase errors, and potentially improve model accuracy and effective resolution.Here, simulations are presented using very high order O3–17 fluxes, with / without high order O2–18 Lagrangian interpolations, pressure gradient / divergence approximations, and SGS turbulent fluxes for a 2D, highly‐viscous (Re ~ 100) diffusion‐limited, nonlinear colliding plumes problem using 25–200 m spatial resolutions. The highest order flux schemes coupled with higher order interpolations, pressure gradient / divergence and SGS flux approximations produced the best solutions, with higher‐order fluxes and interpolations being most important. Overall solution convergence of ~O1–2 with mode‐split (fast sound / slow advective waves) O3 Runge–Kutta temporal schemes was negatively impacted by ≤O1 temporal convergence with SGS fluxes, divergence damping, and especially spatial filters, compared to ~O3 convergence with these inactivated.While very high order schemes were shown to improve solution accuracy, few cost‐effective higher order highly‐viscous test problem solutions (higher order versus finer resolution) were found using theoretical floating‐point operations (FPO) with CFL‐limited or constant stable Courant number‐based time steps. However, employing CPU time, rather than FPOs, demonstrated there was reduced computational burden using higher order approximations. We conclude that O9–17 flux schemes with or without high‐order ≥O4 interpolations, pressure gradient / divergence approximations, and SGS fluxes can improve atmospheric model solution accuracy, without prohibitive computation costs, compared to O3–7 flux with O2 interpolations, pressure gradient / divergence approximations, and SGS fluxes.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:114145
Uncontrolled Keywords:Atmospheric Science
Publisher:Royal Meteorological Society

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation