Nonlinear diffusion-limited two-dimensional colliding-plume simulations with very high-order numerical approximations

Straka, J. M. ORCID: https://orcid.org/0000-0003-3672-5858, Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 and Kanak, K. M. ORCID: https://orcid.org/0000-0003-3479-9669 (2024) Nonlinear diffusion-limited two-dimensional colliding-plume simulations with very high-order numerical approximations. Quarterly Journal of the Royal Meteorological Society, 150 (759). pp. 663-705. ISSN 1477-870X doi: 10.1002/qj.4616

Abstract/Summary

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
URI	https://reading-clone.eprints-hosting.org/id/eprint/114145
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Uncontrolled Keywords	Atmospheric Science
Publisher	Royal Meteorological Society
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