A dynamic variational multiscale method for large eddy simulations on unstructured meshes

Farhat, Charbel; Rajasekharan, Ajaykumar; Koobus, Bruno

doi:10.1016/j.cma.2005.05.045

Cited by 44 publications

(54 citation statements)

References 21 publications

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“…Similar observations are reported for turbulent flow simulations in a diffuser [46]. Moreover, for a VMS method based on a finite volume discretization applied to compressible flows, [24], it was found that the dynamic computation of the Smagorinsky parameter does not improve the results obtained by considering a constant parameter. In view of these experiences, the use of a dynamic model in the VMS methods seems not to be promising at the moment, at least not for second order discretizations.…”

Section: The Turbulence Modelssupporting

confidence: 65%

“…Numerical studies of VMS methods which include a comparison with the classical dynamic Smagorinsky LES model, for instance, in [14,15,18,22,24], show that the VMS methods give in general better results.…”

mentioning

confidence: 97%

“…Turbulent channel flow computations are presented for Re ∈ {180, 590}. For further applications of the VMS idea in the simulation of turbulent flows, we refer to [23,24].…”

mentioning

confidence: 99%

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Simulations of the turbulent channel flow at Re_τ = 180 with projection‐based finite element variational multiscale methods

John

Roland

2007

Numerical Methods in Fluids

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Section: The Turbulence Modelssupporting

confidence: 65%

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confidence: 97%

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Simulations of the turbulent channel flow at Re_τ = 180 with projection‐based finite element variational multiscale methods

John

Roland

2007

Numerical Methods in Fluids

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“…The transient behavior at a given Mach number of the considered F-16 reduced-order aeroelastic model is governed by a set of linearized fluid-structure equations of motion that can be written exactly as in system (31). More specifically, in this case, V and H are two real square matrices of size 20, M q and K q are two real square matrices of size 4, C q is a 20×8 real matrix, P is an 8×20 real matrix, and w and q are two vectors of size 20 and 8, respectively.…”

Section: Benchmark Resultsmentioning

confidence: 99%

Robust and provably second‐order explicit–explicit and implicit–explicit staggered time‐integrators for highly non‐linear compressible fluid–structure interaction problems

Farhat

Rallu

Wang

et al. 2010

Numerical Meth Engineering

101

108

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SUMMARYAn explicit-explicit staggered time-integration algorithm and an implicit-explicit counterpart are presented for the solution of non-linear transient fluid-structure interaction problems in the Arbitrary LagrangianEulerian (ALE) setting. In the explicit-explicit case where the usually desirable simultaneous updating of the fluid and structural states is both natural and trivial, staggering is shown to improve numerical stability. Using rigorous ALE extensions of the two-stage explicit Runge-Kutta and three-point backward difference methods for the fluid, and in both cases the explicit central difference scheme for the structure, secondorder time-accuracy is achieved for the coupled explicit-explicit and implicit-explicit fluid-structure time-integration methods, respectively, via suitable predictors and careful stagings of the computational steps. The robustness of both methods and their proven second-order time-accuracy are verified for sample application problems. Their potential for the solution of highly non-linear fluid-structure interaction problems is demonstrated and validated with the simulation of the dynamic collapse of a cylindrical shell submerged in water. The obtained numerical results demonstrate that, even for fluid-structure applications with strong added mass effects, a carefully designed staggered and subiteration-free time-integrator can achieve numerical stability and robustness with respect to the slenderness of the structure, as long as the fluid is justifiably modeled as a compressible medium.

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“…The coe cients µ n and Ÿ n are calculated element-wise on every high order element oe e for a Galerkin approximation of Equations (91). More specifically, for the sensible temperature T = ◊(p/p 0 ) R/c p and one finite/spectral element of characteristic length h oee , we start by defining the dynamic viscosities…”

Section: Remark 41mentioning

confidence: 99%

A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin

Marras

Kelly²,

Moragues

et al. 2015

Arch Computat Methods Eng

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Numerical Weather Prediction (NWP) is in a period of transition. As resolutions increase, global models are moving towards fully nonhydrostatic dynamical cores, with the local and global models using the same governing equations; therefore we have reached a point where it will be necessary to use a single model for both applications. The new dynamical cores at the heart of these unified models are designed to scale e ciently on clusters with hundreds of thousands or even millions of CPU cores and GPUs. Operational and research NWP codes currently use a wide range of numerical methods: finite di erences, spectral transform, finite volumes and, increasingly, finite/spectral elements and discontinuous Galerkin, which constitute element-based Galerkin (EBG) methods. Due to their important role in this transition, will EBGs be the dominant power behind NWP in the next 10 years, or will they just be one of many methods to choose from? One decade after the review of numerical methods for atmospheric modeling by Steppeler et al. (2003) [Review of numerical methods for nonhydrostatic weather prediction models Meteorol. Atmos. Phys. 82, 2003], this review discusses EBG methods as a viable numerical approach for the next-generation NWP models. One well-known weakness of EBG methods is the generation of unphysical oscillations in advection-dominated flows; special attention is hence devoted to dissipation-based stabilization methods. Since EBGs are geometrically flexible and allow both conforming and non-conforming meshes, as well as grid adaptivity, this review is concluded with a short overview of how mesh generation and dynamic mesh refinement are becoming as important for atmospheric modeling as they have been for engineering applications for many years.

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A dynamic variational multiscale method for large eddy simulations on unstructured meshes

Cited by 44 publications

References 21 publications

Simulations of the turbulent channel flow at Re_τ = 180 with projection‐based finite element variational multiscale methods

Simulations of the turbulent channel flow at Re_τ = 180 with projection‐based finite element variational multiscale methods

Robust and provably second‐order explicit–explicit and implicit–explicit staggered time‐integrators for highly non‐linear compressible fluid–structure interaction problems

A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin

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A dynamic variational multiscale method for large eddy simulations on unstructured meshes

Cited by 44 publications

References 21 publications

Simulations of the turbulent channel flow at Reτ = 180 with projection‐based finite element variational multiscale methods

Simulations of the turbulent channel flow at Reτ = 180 with projection‐based finite element variational multiscale methods

Robust and provably second‐order explicit–explicit and implicit–explicit staggered time‐integrators for highly non‐linear compressible fluid–structure interaction problems

A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin

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Simulations of the turbulent channel flow at Re_τ = 180 with projection‐based finite element variational multiscale methods

Simulations of the turbulent channel flow at Re_τ = 180 with projection‐based finite element variational multiscale methods