Semi-implicit BDF time discretization of the Navier–Stokes equations with VMS-LES modeling in a High Performance Computing framework

Forti, Davide; Dedè, Luca

doi:10.1016/j.compfluid.2015.05.011

Cited by 91 publications

(119 citation statements)

References 48 publications

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“…[7] (see Table 1). To sum up, also the parallel performances in the case of equal-order FE are rather satisfactory, and seem to be in accordance with the current state-of-the-art, e.g., [28].…”

Section: Lid-driven Cavity Flow (3d)supporting

confidence: 64%

Assessment of self-adapting local projection-based solvers for laminar and turbulent industrial flows

et al. 2018

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In this work, we study the performance of some local projection-based solvers in the Large Eddy Simulation (LES) of laminar and turbulent flows governed by the incompressible Navier-Stokes Equations (NSE). On one side, we focus on a high-order term-by-term stabilization Finite Element (FE) method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard Local Projection Stabilization (LPS) methods is replaced by an interpolation-stabilized structure. The interest of LPS methods is that they ensure a self-adapting high accuracy in laminar regions of turbulent flows, which turns to be of overall optimal high accuracy if the flow is fully laminar. On the other side, we propose a new Reduced Basis (RB) Variational Multi-Scale (VMS)-Smargorinsky turbulence model, based upon an empirical interpolation of the sub-grid eddy viscosity term. This method yields dramatical improvements of the computing time for benchmark flows. An overview about known results from the numerical analysis of the proposed methods is given, by highlighting the used mathematical tools. In the numerical study, we have considered two well known problems with applications in industry: the (3D) turbulent flow in a channel and the (2D/3D) recirculating flow in a lid-driven cavity.

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Section: Lid-driven Cavity Flow (3d)supporting

confidence: 64%

Assessment of self-adapting local projection-based solvers for laminar and turbulent industrial flows

et al. 2018

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“…This explains why the overall scalability of the proposed method is satisfactory on a wide range of process counts. To sum up, the parallel performances of the proposed method are rather satisfactory, and seem to be in accordance with the current state-of-the-art, e.g., [34].…”

Section: Parallel Performances Of the Solversupporting

confidence: 60%

“…In this manner, we obtain an efficient, i.e., robust and fast, solver for the HPC of laminar and turbulent flows in the open-source FE software FreeFem++ [45] interfaced with HPDDM. A similar recent study has been performed in [34], where a semi-implicit BDF time discretization scheme for the NSE with residual-based VMS-LES modeling is combined together with a parallel multigrid preconditioner applied on the right and the GMRES iterative method. However, the cited study differs also because it is applied to the monolithic (coupled velocity-pressure) form of the linear system associated to the problem.…”

Section: Introductionmentioning

confidence: 99%

Efficient and scalable discretization of the Navier–Stokes equations with LPS modeling

Haferssas

Jolivet

Rubino

2018

Computer Methods in Applied Mechanics and Engineering

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In this work, we address the solution of the Navier-Stokes equations (NSE) by a Finite Element (FE) Local Projection Stabilization (LPS) method. The focus is on a LPS method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard LPS methods is replaced by an interpolation-stabilized structure, which only acts on the high frequency components of the flow. As a main contribution, we propose and test an efficient discretization of the model via a stable velocity-pressure segregation, using semi-implicit Backward Differentiation Formulas (BDF) in time. On the one hand, numerical studies illustrate that the solver accurately reproduces first and second-order statistics of benchmark turbulent flows for relatively coarse meshes. On the other hand, they show that the solver works in an efficient (i.e., robust and fast) way, especially when interfaced with scalable domain decomposition methods. Such scalability results are obtained on up to 16,384 cores with a near-ideal speedup.

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“…14,15 Some other authors proposed to further split the resolved scales into coarse and fine scales and to adopt the hypothesis that the subscales do not affect the coarse resolved scales. More recently, some authors [18][19][20][21][22] have directly applied the VMS method in order to solve the Navier-Stokes turbulence, in what are called implicit LES (ILES) techniques. More recently, some authors [18][19][20][21][22] have directly applied the VMS method in order to solve the Navier-Stokes turbulence, in what are called implicit LES (ILES) techniques.…”

Section: Introductionmentioning

confidence: 99%

Variational multiscale approximation of the one‐dimensional forced Burgers equation: The role of orthogonal subgrid scales in turbulence modeling

Ballon-Bayona

Baiges

Codina

2017

Numerical Methods in Fluids

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Summary A numerical approximation for the one‐dimensional Burgers equation is proposed by means of the orthogonal subgrid scales–variational multiscale (OSGS‐VMS) method. We evaluate the role of the variational subscales in describing the Burgers “turbulence” phenomena. Particularly, we seek to clarify the interaction between the subscales and the resolved scales when the former are defined to be orthogonal to the finite‐dimensional space. Direct numerical simulation is used to evaluate the resulting OSGS‐VMS energy spectra. The comparison against a large eddy simulation model is presented for numerical discretizations in which the grid is not capable of solving the small scales. An accurate approximation to the phenomena of turbulence is obtained with the addition of the purely dissipative numerical terms given by the OSGS‐VMS method without any modification of the continuous problem.

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Semi-implicit BDF time discretization of the Navier–Stokes equations with VMS-LES modeling in a High Performance Computing framework

Cited by 91 publications

References 48 publications

Assessment of self-adapting local projection-based solvers for laminar and turbulent industrial flows

Assessment of self-adapting local projection-based solvers for laminar and turbulent industrial flows

Efficient and scalable discretization of the Navier–Stokes equations with LPS modeling

Variational multiscale approximation of the one‐dimensional forced Burgers equation: The role of orthogonal subgrid scales in turbulence modeling

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