An LES-like stabilization of the spectral element solution of the euler equations for atmospheric flows
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Authors
Marras, Simone
Giraldo, Francis X.
Müller, Andreas
Subjects
Spectral Element Method
Euler Equations
LES
Stabilization
Non- Hydrostatic Atmospheric Flow
Moist Dynamics
Squall Line Simulations
Euler Equations
LES
Stabilization
Non- Hydrostatic Atmospheric Flow
Moist Dynamics
Squall Line Simulations
Advisors
Date of Issue
2014
Date
Publisher
Language
Abstract
The solution of the Euler equations by the spectral element method (SEM)
is subject to oscillatory behavior if the high-frequency modes are not damped in some
way. In this analysis, we extend to high order spectral elements and to low-Mach number
flows the recent work by Nazarov and Ho↵man [20], where an LES-like physical di↵usion
acts both as a localized and controlled numerical stabilization for finite elements and
as a turbulence model for compressible flows. In the framework of high-order SEM for
the solution of the low-Mach number flows, this approach is a possible physics-based
alternative to the variational multiscale stabilization (VMS) method that the authors
successfully applied to the SEM solution of the advection di↵usion equation [17] in the
context of atmospheric flows. Like for VMS, stabilization is obtained by means of a
residual-based term that is added to the inviscid Euler equations. Unlike VMS, however,
this extra term is based on purely physical –rather than numerical– assumptions, in that
it is related to the viscous component of the stress tensor of the Navier-Stokes equations.
The method is tested with pseudo and fully 3D simulations of idealized nonhydrostatic
atmospheric flows and is verified against data from the literature. This work represents a
step toward the implementation of a stabilized, high order, spectral element LES model
within the Nonhydrostatic Unified Model of the Atmosphere (NUMA) developed by the
authors.
Type
Article
Description
Series/Report No
Department
Applied Mathematics
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11th World Congress on Computational Mechanics (WCCM XI)
5th European Conference on Computational Mechanics (ECCM V)
6th European Conference on Computational Fluid Dynamics (ECFD VI)
E. O˜nate, J. Oliver and A. Huerta (Eds)
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.