TY - JOUR
T1 - A parameter-free dynamic alternative to hyper-viscosity for coupled transport equations
T2 - Application to the simulation of 3D squall lines using spectral elements
AU - Marras, Simone
AU - Giraldo, Francis X.
N1 - Funding Information:
The authors are thankful to Dr. Hilary Weller (U. Reading, UK), Dr. Guillaume Houzeaux (Barcelona Supercomputing Center, Spain), and one anonymous reviewer for important inputs that helped improve this article. The authors gratefully acknowledge the support of the Office of Naval Research through program element PE-0602435N , the National Science Foundation (Division of Mathematical Sciences) through program element 121670 . The work of the first author was carried out through the National Research Council (NRC) Research Associateship Programs of the National Academies.
Publisher Copyright:
© 2014 Elsevier Inc.
PY - 2015/2/5
Y1 - 2015/2/5
N2 - 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) (Marras et al. (2012) [7]) 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.
AB - 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) (Marras et al. (2012) [7]) 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.
KW - Crosswind discontinuity capturing
KW - Deep convection
KW - Dynamic artificial diffusion
KW - Hyper-viscosity
KW - Kessler microphysics
KW - Monotonicity-preserving high-order methods
KW - Residual-based stabilization
KW - Spectral element method
KW - Stabilization of spectral elements
KW - VMM
KW - VMS
KW - Variational multiscale method
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U2 - 10.1016/j.jcp.2014.11.046
DO - 10.1016/j.jcp.2014.11.046
M3 - Article
AN - SCOPUS:84918806518
SN - 0021-9991
VL - 283
SP - 360
EP - 373
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -