Expanding Grids for Efficient Cloud Dynamics Simulations Across Scales

David H Marsico,Samuel N Stechmann

doi:10.1515/mcwf-2020-0101

Abstract

Abstract With large eddy simulations (LES) and/or cloud-resolving models (CRMs), it is now possible to simultaneously simulate shallow and deep convection. However, using traditional methods, the computational expense is typically very large, due to the small grid spacings needed to resolve shallow clouds. Here, the main purpose is to present a method that is computationally less expensive by a factor of roughly 10 to 50. Unlike traditional grid stretching of only the vertical z grid spacing, the present method involves expansion of the grid spacing in all coordinate directions (x,y,z) and time t. A ˝ne grid spacing of O(10)-O(100) m can be used near the surface to resolve boundary layer turbulence, and the grid spacing expands to be O(1000) m at higher altitudes, which reduces computational cost while still resolving deep convection. Example simulations are conducted with a simpli˝ed LES/CRM in 2D to verify the theoretical cost savings.

Highlights

Clouds and convection occur across a range of scales, and the grid spacing needed in numerical simulations can be di erent for di erent cloud phenomena
Is a small grid spacing needed to resolve shallow clouds, but a large domain is needed to encompass the scales of deep convective clouds
In contrast to the common approach of stretching of a grid in only the vertical z direction, the present method involves an expansion of the grid spacing in all coordinate directions x, y, z and time t, which brings additional computational savings

Summary

Introduction

Clouds and convection occur across a range of scales, and the grid spacing needed in numerical simulations can be di erent for di erent cloud phenomena. The setup of the expanding grid could be useful in any setting where shallow clouds and deep convection are simulated together. What we observe in numerical simulations is somewhat close to this: the expanding grid requires more computation time than the coarse grid by a factor of O( ) for the three di erent domain sizes. This factor of 700–1000 is small in a relative sense; if one instead re nes the uniform coarse grid to the uniform ne grid, the additional expense is theoretically a factor of roughly 33,000. Compared to the coarse grid, the equivalent grid features the same abrupt transition to deep convection, with an extremely strong updraft

Conclusions

A Appendix

B Appendix