Resolution of d’Alembert’s Paradox

Hoffman, Johan; Johnson, Claes

doi:10.1007/s00021-008-0290-1

Cited by 41 publications

(39 citation statements)

References 14 publications

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“…The presented results support the theory of lift force generation by Hoffman and Johnson published in [1,2], however they could not be considered as the final and decisive confirmation.…”

Section: Discussionsupporting

confidence: 69%

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On 3D flow-structures behind an inclined plate

et al. 2017

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Abstract. Stereo PIV measurements has been performed behind the inclined plate, angle of attack 5 and 10 deg. Occurrence and dynamics of streamwise structures behind the plate trailing edge have been studied in details using POD method. The streamwise structures are represented by vortices and low-and highvelocity regions, probably streaks. The obtained results support the hypothesis of an airfoil-flow force interaction

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“…The presented results support the theory of lift force generation by Hoffman and Johnson published in [1,2], however they could not be considered as the final and decisive confirmation.…”

Section: Discussionsupporting

confidence: 69%

“…The motivation of the presented study is supporting new ideas about principle of flight by Hoffman and Johnson from KTH Stockholm, see [1,2]. The new hypothesis of physical mechanism of flight relies on existence of streamwise vortical structures on the suction side of the airfoil and within its wake.…”

Section: Introductionsupporting

confidence: 66%

On 3D flow-structures behind an inclined plate

et al. 2017

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“…More generally, we present evidence that all (non-trivial) initially smooth Euler solutions exhibit blowup into turbulent solutions. This work closely connects to the new resolution of d'Alembert's paradox presented in [15].…”

Section: The Clay Navier-stokes Millennium Problemsupporting

confidence: 64%

Blow up of incompressible Euler solutions

Hoffman

Johnson

2008

Bit Numer Math

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“…We have presented evidence in the form of analysis and computational studies, that the macroscopic features of high Reynolds number flow, including 3D flow separation, is mainly determined by large scale stability aspects, rather than boundary layer effects [19,[1][2][3]5]. …”

Section: Boundary Conditionsmentioning

confidence: 99%

“…The parameter-free aspect (iii) of DFS is related to the fact that no subgrid scale stresses or Reynolds stresses are parametrized as in LES (Large Eddy Simulation) or RANS (Reynolds Averaged Navier-Stokes equations) [16], and that for high Reynolds numbers we assume that the skin friction of the boundary layers is dominated by inertial effects, so that a free slip boundary condition is used at solid boundaries [17][18][19]. In contrast to RANS and LES, no averaging or filtering operators are introduced in DFS, the resolution of the turbulent scales is determined as part of the computation, with the local mesh size adapted based on the required precision in the chosen quantity of interest.…”

Section: Introductionmentioning

confidence: 99%

Towards a parameter-free method for high Reynolds number turbulent flow simulation based on adaptive finite element approximation

Hoffman

Jansson

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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Highlights• We present a parameter-free method for high Reynolds number turbulent flow.• The method is based on adaptive mesh optimization using adjoint techniques.• We connect the numerical approximation to dissipative weak solutions.• Turbulent boundary layers are left unresolved, no boundary layer mesh is needed.• We highlight benchmark problems for which the method is validated. AbstractThis article is a review of our work towards a parameter-free method for simulation of turbulent flow at high Reynolds numbers. In a series of papers we have developed a model for turbulent flow in the form of weak solutions of the Navier-Stokes equations, approximated by an adaptive finite element method, where: (i) viscous dissipation is assumed to be dominated by turbulent dissipation proportional to the residual of the equations, and (ii) skin friction at solid walls is assumed to be negligible compared to inertial effects. The result is a computational model without empirical data, where the only model parameter is the local size of the finite element mesh. Under adaptive refinement of the mesh based on a posteriori error estimation, output quantities of interest in the form of functionals of the finite element solution converge to become independent of the mesh resolution, and thus the resulting method has no adjustable parameters. No ad hoc design of the mesh is needed, instead the mesh is optimized based on solution features, in particular no boundary layer mesh is needed. We connect the computational method to the mathematical concept of a dissipative weak solution of the Euler equations, as a model of high Reynolds number turbulent flow, and we highlight a number of benchmark problems for which the method is validated. The purpose of the article is to present the computational framework in a concise form, to report on recent progress, and to discuss open problems that are subject to ongoing research.

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Resolution of d’Alembert’s Paradox

Cited by 41 publications

References 14 publications

On 3D flow-structures behind an inclined plate

On 3D flow-structures behind an inclined plate

Blow up of incompressible Euler solutions

Towards a parameter-free method for high Reynolds number turbulent flow simulation based on adaptive finite element approximation

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