A Parameter-Free Dynamic Alternative to Hyper-Viscosity for Coupled Transport Equations: Application to the Simulation of 3D Squall Lines Using Spectral Elements
Giraldo, Francis X.
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The stabilization of high order spectral elements to solve the transport equations for tracers in the atmosphere remains an active topic of research among atmospheric modelers. This paper builds on our previous work on variational multiscale stabilization (VMS) and discontinuity capturing (DC) [Variational multiscale stabilization of high-order spectral elements for the advection-di↵usion equation J. Comput. Phys. 231 (2012) 7187-7213] and shows the applicability of VMS+DC to realistic atmospheric problems that involve physics coupling with phase change in the simulation of 3D deep convection. We show that the VMS+DC approach is a robust technique that can damp the high order modes characterizing the spectral element solution of complex coupled transport problems. 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 flow direction, 3) it is numerically consistent, and 4) it can improve the monotonicity of high-order spectral elements. The proposed method is assessed by comparing the results against those obtained with a fourth-order hyper-viscosity programmed in the same code. The main conclusion that arises is that tuning can be fully avoided without loss of accuracy if the dissipative scheme is properly designed. Finally, the cost of parallel communication is that of a second order operator which means 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 importance as we approach the exascale range of computing.
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Marras, Simone; Nazarov, Murtazo; Giraldo, Francis X. (ACM, 2015);The high order spectral element approximation of the Euler equations is stabilized via a dynamic sub-grid scale model (Dyn-SGS). This model was originally designed for linear finite elements to solve compressible flows ...
Physics-based stabilization of spectral elements for the 3D euler equations of moist atmospheric convection Marras, Simone; Müller, Andreas; Giraldo, Francis X. (2014);In the context of stabilization of high order spectral elements, we introduce a dissipative scheme based on the solution of the compressible Euler equations that are regularized through the addition of a residual-based ...
LES-like stabilization of spectral elements for the solution of the Euler equations of moist stratified flows Marras, Simone; Mueller, Andreas; Giraldo, Francis X. (Monterey, California. Naval Postgraduate School, 2014-10);The solution of the Euler equations by the spectral element method is prone to instabilities that must be damped in some way. We approach the problem of stabilization via an adaptive Large-Eddy-Simulation-like scheme meant ...