## 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 language | English (US) |
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Title of host publication | 11th 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 |

Editors | Antonio Huerta, Eugenio Onate, Xavier Oliver |

Publisher | International Center for Numerical Methods in Engineering |

Pages | 5722-5743 |

Number of pages | 22 |

ISBN (Electronic) | 9788494284472 |

State | Published - Jul 1 2014 |

Externally published | Yes |

Event | Joint 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 2014 → Jul 25 2014 |

### Publication series

Name | 11th 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 |
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### Other

Other | Joint 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 |
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Country/Territory | Spain |

City | Barcelona |

Period | 7/20/14 → 7/25/14 |

## 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