A Parameter-Free Dynamic Alternative to Hyper-Viscosity for Coupled Transport Equations: Application to the Simulation of 3D Squall Lines Using Spectral Elements

摘要

The stabilization of high order spectral elements to solve the transport equations for tracers in theatmosphere remains an active topic of research among atmospheric modelers. This paper buildson our previous work on variational multiscale stabilization (VMS) and discontinuity capturing(DC) [Variational multiscale stabilization of high-order spectral elements for the advection-di↵usionequation J. Comput. Phys. 231 (2012) 7187-7213] and shows the applicability of VMS+DC torealistic atmospheric problems that involve physics coupling with phase change in the simulationof 3D deep convection. We show that the VMS+DC approach is a robust technique that can dampthe high order modes characterizing the spectral element solution of complex coupled transportproblems. The method has important properties that techniques of more common use often lack:1) it is free of a user-defined parameter, 2) it is anisotropic in that it only acts along the flowdirection, 3) it is numerically consistent, and 4) it can improve the monotonicity of high-orderspectral elements. The proposed method is assessed by comparing the results against those obtainedwith a fourth-order hyper-viscosity programmed in the same code. The main conclusion that arisesis that tuning can be fully avoided without loss of accuracy if the dissipative scheme is properlydesigned. Finally, the cost of parallel communication is that of a second order operator whichmeans that fewer communications are required by VMS+DC than by a hyper-viscosity method;fewer communications translate into a faster and more scalable code, which is of vital importanceas we approach the exascale range of computing.