Computation of Mean Drag for Bluff Body Problems Using Adaptive DNS/LES

Hoffman, Johan

doi:10.1137/040614463

Cited by 50 publications

(59 citation statements)

References 13 publications

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“…This methodology is validated for a number of standard benchmark problems in the literature, 4,5,6,7 and in the following sections we describe the basic elements of the G2 method, also referred to as Adaptive DNS/LES, or simply Direct finite element simulation (DFS). For the particular problem proposed in the HiLiftPW-2, we used a low order finite element discretization on unstructured tetrahedral meshes, which we refer to as cG (1) …”

Section: Simulation Methodologymentioning

confidence: 99%

Time-resolved adaptive FEM simulation of the DLR-F11 aircraft model at high Reynolds number

Hoffman

Jansson

et al. 2014

52nd Aerospace Sciences Meeting

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We present a time-resolved, adaptive finite element method for aerodynamics, together with the results from the HiLiftPW-2 workshop, where this method is used to compute the flow past a DLR-F11 aircraft model at realistic Reynolds number. The mesh is automatically constructed by the method as part of the computation, and no explicit turbulence model is used. The effect of unresolved turbulent boundary layers is modeled by a simple parametrization of the wall shear stress in terms of the skin friction. In the extreme case of very high Reynolds numbers we approximate the small skin friction by zero skin friction, corresponding to a free slip boundary condition, which results in a computational model without any model parameter that needs tuning. Thus, the simulation methodology bypasses the main challenges posed by high Reynolds number CFD: the design of an optimal computational mesh, turbulence (or subgrid) modeling, and the cost of boundary layer resolution. The results from HiLiftPW-2 presented in this report show good agreement with experimental data for a range of different angles of attack, while using orders of magnitude fewer degrees of freedom than what is needed in state of the art methods such as RANS.

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Section: Simulation Methodologymentioning

confidence: 99%

Time-resolved adaptive FEM simulation of the DLR-F11 aircraft model at high Reynolds number

Hoffman

Jansson

et al. 2014

52nd Aerospace Sciences Meeting

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“…For this case, viscous effects are not negligible so that the viscosity is kept in the model (1), and no slip boundary conditions are chosen where the velocity is set to zero on the solid boundary Γ . DFS in the form of the cG(1)cG(1) method has been validated for a number of model problems of simple geometry bluff bodies, including a surface mounted cube and a rectangular cylinder [12,11], a sphere [13] and a circular cylinder [14]. In each case, convergence is observed for output quantities such as drag, lift and pressure coefficients, and Strouhal numbers, and the adaptive algorithm leads to an efficient method often using orders of magnitude fewer number of degrees of freedom compared to LES methods based on ad hoc design of the mesh.…”

Section: Medium Reynolds Number Flowmentioning

confidence: 99%

“…This local energy equation connects to a dissipative weak Euler solution [33], with inertial energy dissipation resulting from local non-smoothness of the solution, and not from any viscosity. The dissipative term D n h (Û ) in (13) reflects local non-smoothness in the solution identified by the residuals, and is observed to be independent of h under sufficient mesh resolution [12,15] …”

Section: Residual Based Numerical Dissipation and Withmentioning

confidence: 99%

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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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“…To solve the Euler equations computationaly we use an adaptive finite element method referred to as EG2 with a duality-based a posteriori error control of drag/lift presented in detail in [25,20,21,23,24], and in executable form available from the Unicorn-project under FEniCS [37], allowing direct verification of the computational results of this note.…”

Section: Introductionmentioning

confidence: 99%

Resolution of d’Alembert’s Paradox

Hoffman¹,

Johnson²

2008

J. Math. Fluid Mech.

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We propose a resolution of d'Alembert's Paradox comparing observation of substantial drag/lift in fluids with very small viscosity such as air and water, with the mathematical prediction of zero drag/lift of stationary irrotational solutions of the incompressible inviscid Euler equations, referred to as potential flow. We present analytical and computational evidence that (i) potential flow cannot be observed because it is illposed or unstable to perturbations, (ii) computed viscosity solutions of the Euler equations with slip boundary conditions initiated as potential flow, develop into turbulent solutions which are wellposed with respect to drag/lift and which show substantial drag/lift, in accordance with observations.

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Computation of Mean Drag for Bluff Body Problems Using Adaptive DNS/LES

Cited by 50 publications

References 13 publications

Time-resolved adaptive FEM simulation of the DLR-F11 aircraft model at high Reynolds number

Time-resolved adaptive FEM simulation of the DLR-F11 aircraft model at high Reynolds number

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

Resolution of d’Alembert’s Paradox

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