Space–time adaptive simulations for unsteady Navier–Stokes problems

Berrone, Stefano; Marro, Massimo

doi:10.1016/j.compfluid.2008.11.004

Cited by 34 publications

(33 citation statements)

References 44 publications

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“…(24), we proceed to the next timestep because we are sure the current solution has a suitable accuracy and re-computing a new solution with an enlarged Δt n would not give any advantage; therefore, we enlarge Δt n for the next timestep. Some other details about the implemented adaptive algorithm are described in [9].…”

Section: Adaptive Algorithmmentioning

confidence: 99%

“…Among the theoretical analyses, Bernardi and Verfürth [4] performed the a posteriori analysis of the time-dependent Stokes equations, Verfürth considered the nonstationary convection-diffusion equations [30] and the heat equation [28] and Picasso [20] analysed the adaptivity for linear parabolic problems. Adaptive numerical investigations were also performed in [9] for Navier-Stokes laminar flows and in [6] for the heat equation. In [8] a new approach to space-time adaptivity resorts to local-in-space timestep-lengths for each element.…”

Section: Introductionmentioning

confidence: 99%

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Numerical investigation of effectivity indices of space-time error indicators for Navier–Stokes equations

Berrone

Marro

2010

Computer Methods in Applied Mechanics and Engineering

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Section: Adaptive Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical investigation of effectivity indices of space-time error indicators for Navier–Stokes equations

Berrone

Marro

2010

Computer Methods in Applied Mechanics and Engineering

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“…Their method would have been considered in the fields of mesh generation, shape optimization, and computational fluid dynamics. Berrone and Marro (2009) presented space-time adaptive simulations for unsteady Navier-Stokes problems. The fluid domain was discretized by structured triangular finite element mesh and the unsteady flow was traced with a posteriori estimates and adaptive algorithms.…”

Section: Introductionmentioning

confidence: 99%

Dynamic adaptive finite element analysis of acoustic wave propagation due to underwater explosion for fluid-structure interaction problems

Emamzadeh

Ahmadi

Mohammadi

et al. 2015

J. Marine. Sci. Appl.

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In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes: a) calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b) fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c) adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.

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“…In the continuous Galerkin case, this indicator has also been used in [10,9]; obviously, the last term is identically zero in this case. For the hybrid cdG case, the last term will only be positive on improper faces.…”

Section: Error Indicatorsmentioning

confidence: 99%

Adaptive Finite Element Simulation of Incompressible Flows by Hybrid Continuous-Discontinuous Galerkin Formulations

Badia¹,

Baiges²

2013

SIAM J. Sci. Comput.

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Abstract. In this work we design hybrid continuous-discontinuous finite element spaces that permit discontinuities on non-matching element interfaces of non-conforming meshes. Then, we develop an equal-order stabilized finite element formulation for incompressible flows over these hybrid spaces, which combines the element interior stabilization of SUPGtype continuous Galerkin formulations and the jump stabilization of discontinuous Galerkin formulations. Optimal stability and convergence results are obtained. For the adaptive setting, we use an standard error estimator and marking strategy. Numerical experiments show the optimal accuracy of the hybrid algorithm both for uniformly and adaptively refined non-conforming meshes. The outcome of this work is a finite element formulation that can naturally be used on nonconforming meshes, as discontinuous Galerkin formulations, while keeping the much lower CPU cost of continuous Galerkin formulations.Key words. Incompressible flows, adaptive refinement, continuous-discontinuous Galerkin, equal-order interpolation, stabilization AMS subject classifications. 65N30, 35Q61, 65N121. Introduction. The dynamics of incompressible flows are governed by the incompressible Navier-Stokes equations, a set of nonlinear partial differential equations with a dissipative structure. Its numerical approximation is a challenging task. In the asymptotic regime of increasing Reynolds numbers the flow becomes chaotic (turbulent); mathematically, this is a singular limit with a coercivity loss [21]. On the other hand the system has a saddle-point (indefinite) structure, i.e. pressure stability relies on an inf-sup condition [37]. Galerkin finite element (FE) approximations that satisfy a discrete inf-sup condition can solve the second issue but the coercivity loss constrains one to capture all the spatial scales of the flow, i.e. to reduce the computational mesh size up to the Kolmogorov microscale, which is unaffordable in many realistic applications due to limited computational resources.Both issues can be solved by using residual-based FE stabilization techniques of SUPG-type [25,26,17,19]. These formulations make use of continuous FE spaces of functions, denoted as cG (continuous Galerkin) formulations onwards. The idea of these methods is to add to the Galerkin terms additional stabilizing terms that depend on the residual on the element interiors, keeping accuracy whereas improving stability. Stability does not depend on a discrete inf-sup condition anymore, and equal-order approximations can be used. Even for the Stokes problem, where the convective term does not appear, equal-order interpolation is very appealing in terms of implementation issues (simplicity of data-bases and matrix graphs) but also more efficient than inf-sup stable counterparts [31].Another approach to this problem is the use of non-conforming methods based on nodal discontinuous Galerkin (dG) techniques [16,22,34]. Convection stabilization is attained via a proper definition of the numerical fluxes [15,38]. Again, ...

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Space–time adaptive simulations for unsteady Navier–Stokes problems

Cited by 34 publications

References 44 publications

Numerical investigation of effectivity indices of space-time error indicators for Navier–Stokes equations

Numerical investigation of effectivity indices of space-time error indicators for Navier–Stokes equations

Dynamic adaptive finite element analysis of acoustic wave propagation due to underwater explosion for fluid-structure interaction problems

Adaptive Finite Element Simulation of Incompressible Flows by Hybrid Continuous-Discontinuous Galerkin Formulations

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