A variational multiscale stabilized finite element method for the solution of the Euler equations of nonhydrostatic stratified flows

Marras, Simone; Moragues, Margarida; Vázquez, Mariano; Jorba, Oriol; Houzeaux, Guillaume

doi:10.1016/j.jcp.2012.10.056

Cited by 29 publications

(26 citation statements)

References 62 publications

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“…Without the large viscosity that homogenizes the solution as done in [48] with the sole target of reaching convergence, the inviscid, non-linear, and non-steady solution that we present here is not expected to show signs of space-convergence. The same behavior was observed in [41], where VMS was used to stabilize a finite element discretization of the Euler equations. Rather, we expect more and more structures to be resolved until a grid resolution of the order of the smallest eddies is …”

Section: 1 2 D Density Currentsupporting

confidence: 61%

Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

Marras

Nazarov

Giraldo

2015

Journal of Computational Physics

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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 at large Mach numbers. We extend its application to high-order spectral elements to solve the Euler equations of low Mach number stratified flows. The major justification of this work is twofold: stabilization and large eddy simulation are achieved via one scheme only.Because the di usion coe cients of the regularization stresses obtained via Dyn-SGS are residual-based, the e ect of the artificial di usion is minimal in the regions where the solution is smooth. The direct consequence is that the nominal convergence rate of the high-order solution of smooth problems is not degraded. To our knowledge, this is the first application in atmospheric modeling of a spectral element model stabilized by an eddy viscosity scheme that, by construction, may fulfill stabilization requirements, can model turbulence via LES, and is completely free of a user-tunable parameter.From its derivation, it will be immediately clear that Dyn-SGS is independent of the numerical method; it could be implemented in a discontinuous Galerkin, finite volume, or other environments alike. Preliminary discontinuous Galerkin results are reported as well. The straightforward extension to non-linear scalar problems is also described. A suite of 1D, 2D, and 3D test cases is used to assess the method, with some comparison against the results obtained with the most known Lilly-Smagorinsky SGS model.

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Section: 1 2 D Density Currentsupporting

confidence: 61%

Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

Marras

Nazarov

Giraldo

2015

Journal of Computational Physics

Self Cite

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“…These include, but are not limited to the streamline-upwind/Petrov-Galerkin (SUPG) type artificial viscosity [17,18,19,20], the Variational Multi-scale method (VMS) [21,22], localized artificial diffusivity using physical principles [10,11,23,24,25,26,27], the residual based artificial viscosity [14,15,28,29,30], the entropy artificial viscosity [16,31,32], the spectral vanishing viscosity [12,33], and the Laplacian artificial viscosity [13,34,35,36]. Other studies of the artificial viscosity methods can be found in References [37,38,39,40,41], just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Localized Artificial Viscosity Stabilization of Discontinuous Galerkin Methods for Nonhydrostatic Mesoscale Atmospheric Modeling

Giraldo

Peng

et al. 2015

Monthly Weather Review

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Gibbs oscillation can show up near flow regions with strong temperature gradients in the numerical simulation of nonhydrostatic (NH) mesoscale atmospheric flows when using the highorder discontinuous Galerkin (DG) method. We propose to incorporate localized Laplacian artificial viscosity in the DG framework to suppress the spurious oscillation in the vicinity of sharp thermal fronts, while not contaminating the smooth flow features elsewhere. The resulting numerical formulation is then validated on several benchmark test cases, including a shock discontinuity problem with the 1D Burger's equation, and two test cases for the compressible Euler equations: a rising thermal bubble and density current. The results indicate that the proposed DG-localized Laplacian artificial viscosity method works robustly with a wide range of grid sizes and polynomial orders.

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“…When additional numerical stabilisation is required, we usually follow the so-called Variational MultiScale method (see for instance [14] for incompressible or [20] compressible flows). Time is discretized using finite differences to obtain either explicit or implicit schemes of different orders.…”

Section: Computational Mechanics Equationsmentioning

confidence: 99%

Alya: Multiphysics engineering simulation toward exascale

Vázquez

Houzeaux

Korić

et al. 2016

Journal of Computational Science

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180

111

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Abstract. Alya is a multi-physics simulation code developed at Barcelona Supercomputing Center (BSC). From its inception Alya code is designed using advanced High Performance Computing programming techniques to solve coupled problems on supercomputers efficiently. The target domain is engineering, with all its particular features: complex geometries and unstructured meshes, coupled multi-physics with exotic coupling schemes and physical models, ill-posed problems, flexibility needs for rapidly including new models, etc. Since its beginnings in 2004, Alya has scaled well in an increasing number of processors when solving single-physics problems such as fluid mechanics, solid mechanics, acoustics, etc. Over time, we have made a concerted effort to maintain and even improve scalability for multi-physics problems. This poses challenges on multiple fronts, including: numerical models, parallel implementation, physical coupling models, algorithms and solution schemes, meshing process, etc. In this paper, we introduce Alya's main features and focus particularly on its solvers. We present Alya's performance up to 100.000 processors in Blue Waters, the NCSA supercomputer with selected multi-physics tests that are representative of the engineering world. The tests are incompressible flow in a human respiratory system, low Mach combustion problem in a kiln furnace, and coupled electro-mechanical contraction of the heart. We show scalability plots for all cases and discuss all aspects of such simulations, including solver convergence.Key words. Multi-physics coupling, Parallelisation, Computational Mechanics 1. Introduction. Across a range of engineering fields, the use of computational models is pervasive in the whole design and manufacturing process. In complex systems, High Performance Computing (HPC) plays an essential role in simulation and modelling. Researchers and manufacturing teams depend on HPC to create safe cars and energy-efficient aircraft as well as effective communication systems and efficient supply chain models. Availability of advanced HPC technologies has also fundamentally altered the investigative paradigm in the field of biomechanics. But paradoxically, for many engineers and researchers, the existing hardware and software cannot be used to solve their problems. There are many reasons why this happens, but we focus here in only two. On one hand, current HPC systems lack the computational power, network bandwidth and data storage needed for solving tomorrow's real-world engineering challenges. On the other hand, while emerging peta-scale computing is already a strategic enabler of large-scale simulations in many scientific areas (such as astronomy, biology and chemistry), even the most powerful hardware will fail to deliver on its full potential unless matched with simulation software designed specifically for such environments.Several papers describe the effort of performing large-scale simulations on supercomputers, covering key areas: molecular dynamics [26], mantle convection in solid earth dynami...

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A variational multiscale stabilized finite element method for the solution of the Euler equations of nonhydrostatic stratified flows

Cited by 29 publications

References 62 publications

Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

Localized Artificial Viscosity Stabilization of Discontinuous Galerkin Methods for Nonhydrostatic Mesoscale Atmospheric Modeling

Alya: Multiphysics engineering simulation toward exascale

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