A high-order multiscale approach to turbulence for compact nodal schemes

Navah, Farshad; Plata, Marta de la Llave; Couaillier, Vincent

doi:10.1016/j.cma.2020.112885

Cited by 7 publications

(5 citation statements)

References 46 publications

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“…In [4], Bando et al have performed computations of compressible homogeneous isotropic turbulence, showing the good performance of the DG-VMS approach with respect to an implicit LES approach based on an entropy-bounded DG scheme [50]. Based on the aforementioned works, Navah et al [62] have recently derived a general formulation that extends the VMS method for compressible LES to the family of compact nodal methods represented by the high-order flux reconstruction scheme [36,37]. Finally, the spectral properties of the DG-VMS approach have been studied in detail by Naddei et al [58].…”

Section: Introductionmentioning

confidence: 99%

On the performance of a high-order multiscale DG approach to LES at increasing Reynolds number

2019

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The variational multiscale (VMS) approach based on a high-order discontinuous Galerkin (DG) method is used to perform LES of the sub-critical flow past a circular cylinder at Reynolds 3 900, 20 000 and 140 000. The effect of the numerical flux function on the quality of the LES solutions is also studied in the context of very coarse discretizations of the TGV configuration at Re = 20 000. The potential of using p-adaption in combination with DG-VMS is illustrated for the cylinder flow at Re = 140 000 by considering a non-uniform distribution of the polynomial degree based on a recently developed error estimation strategy [59]. The results from these tests demonstrate the robustness of the DG-VMS approach with increasing Reynolds number on a highly curved geometrical configuration.

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Section: Introductionmentioning

confidence: 99%

On the performance of a high-order multiscale DG approach to LES at increasing Reynolds number

2019

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“…Here, t * = t/t c is the non-dimensional time variable and t c = L/v ∞ is the characteristic time. The analysis of the equation describing the temporal evolution of the kinetic energy allows the estimation of numerical errors through the comparison of each of the components of the kinetic energy balance equation [40] which are defined as follows…”

Section: Taylor-green-vortexmentioning

confidence: 99%

“…In this work, a quadrature of degree 10 is used to assess the ensemble averages. As in [16,40] the error estimator δ may be expressed as…”

Section: Taylor-green-vortexmentioning

confidence: 99%

The Spectral Difference Raviart–Thomas Method for Two and Three-Dimensional Elements and Its Connection with the Flux Reconstruction Formulation

2022

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The purpose of this work is to describe in detail the development of the spectral difference Raviart-Thomas (SDRT) formulation for two and three-dimensional tensor-product elements and simplexes. Through the process, the authors establish the equivalence between the SDRT method and the flux reconstruction (FR) approach under the assumption of the linearity of the flux and the mesh uniformity. Such a connection allows building a new family of FR schemes for two and three-dimensional simplexes and also to recover the well-known FR-SD method with tensor-product elements. In addition, a thorough analysis of the numerical dissipation and dispersion of both aforementioned schemes and the nodal discontinuous Galerkin FR (FR-DG) method with two and three-dimensional elements is proposed through the use of the combined-mode Fourier approach. SDRT is shown to possess an enhanced temporal linear stability in comparison to FR-DG. On the contrary, SDRT displays larger dissipation and dispersion errors with respect to FR-DG. Finally, the study is concluded with a set of numerical experiments, the linear advection-diffusion problem, the Isentropic Euler Vortex, and the Taylor-Green Vortex (TGV). The latter test case shows that SDRT schemes present a non-linear unstable behavior with simplex elements and certain polynomial degrees. For the sake of completeness, the matrix form of the SDRT method is developed and the computational performance of SDRT with respect to FR schemes is evaluated using GPU architectures.

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“…Here, t * = t/t c is the non-dimensional time variable and t c = L/v ∞ is the characteristic time. The analysis of the equation describing the temporal evolution of the kinetic energy allows to estimate numerical errors by the comparison of each of components of the kinetic energy balance equation [35] which are defined as follows…”

Section: Taylor-green-vortexmentioning

confidence: 99%

“…In this work, a quadrature of degree 10 is used to assess the ensemble averages. As in [35,14] the error estimator δ may be expressed as…”

Section: Taylor-green-vortexmentioning

confidence: 99%

The Spectral Difference Raviart-Thomas method for two and three-dimensional elements and its connection with the Flux Reconstruction formulation

Sáez-Mischlich¹,

Sierra²,

Gressier³

2021

Preprint

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The purpose of this work is to describe in detail the development of the Spectral Difference Raviart-Thomas (SDRT) formulation for two and three-dimensional tensor-product elements and simplexes. Through the process, the authors establish the equivalence between the SDRT method and the Flux-Reconstruction (FR) approach under the assumption of the linearity of the flux and the mesh uniformity. Such a connection allows to build a new family of FR schemes for two and three-dimensional simplexes and also to recover the well-known FR-SD method with tensor-product elements. In addition, a thorough analysis of the numerical dissipation and dispersion of both aforementioned schemes and the nodal Discontinuous Galerkin FR (FR-DG) method with two and three-dimensional elements is proposed through the use of the combined-mode Fourier approach. SDRT is shown to posses an enhanced temporal linear stability regarding the FR-DG. On the contrary, SDRT displays larger dissipation and dispersion errors with respect to FR-DG. Finally, the study is concluded with a set of numerical experiments, the linear advection-diffusion problem, the Isentropic Euler Vortex and the Taylor-Green Vortex (TGV). The latter test case shows that SDRT schemes present a non-linear unstable behavior with simplex elements and certain polynomial degrees. For the sake of completeness, the matrix form of the SDRT method is developed and the computational performance of SDRT with respect to FR schemes is evaluated using GPU architectures.

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A high-order multiscale approach to turbulence for compact nodal schemes

Cited by 7 publications

References 46 publications

On the performance of a high-order multiscale DG approach to LES at increasing Reynolds number

On the performance of a high-order multiscale DG approach to LES at increasing Reynolds number

The Spectral Difference Raviart–Thomas Method for Two and Three-Dimensional Elements and Its Connection with the Flux Reconstruction Formulation

The Spectral Difference Raviart-Thomas method for two and three-dimensional elements and its connection with the Flux Reconstruction formulation

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