An les-like stabilization of the spectral element solution of the euler equations for atmospheric flows

Simone Marras, Andreas Müller, Francis X. Giraldo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

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 Hoffman [20], where an LES-like physical diffusion 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 diffusion 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.

Original languageEnglish (US)
Title of host publication11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014
EditorsAntonio Huerta, Eugenio Onate, Xavier Oliver
PublisherInternational Center for Numerical Methods in Engineering
Pages5722-5743
Number of pages22
ISBN (Electronic)9788494284472
StatePublished - Jul 1 2014
Externally publishedYes
EventJoint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014 - Barcelona, Spain
Duration: Jul 20 2014Jul 25 2014

Publication series

Name11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014

Other

OtherJoint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014
CountrySpain
CityBarcelona
Period7/20/147/25/14

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Computational Theory and Mathematics
  • Computer Science Applications
  • Mechanical Engineering

Keywords

  • Euler equations
  • LES
  • Moist dynamics
  • Non-hydrostatic atmospheric flow
  • Spectral element method
  • Squall line simulations
  • Stabilization

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