A new approach to computational turbulence modeling

Hoffman, Johan; Johnson, Claes

doi:10.1016/j.cma.2004.09.015

Cited by 94 publications

(90 citation statements)

References 8 publications

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“…For example, the widely used Smagorinsky subgrid model [21] is closely related to methods of artificial viscosity used to stabilize numerical methods [22]. To tackle this issue, different approaches have been attempted, from using high order numerical methods with minimal dissipation, to interpreting the numerical stabilization as the subgrid model [23,11,24,25], or alternatively trying to balance the two sources of errors [26,10]. The relationship between the local resolution of the computational mesh and the turbulent length scales of RANS and LES also poses challenges, in particular near solid walls where small turbulent scales dictate a very fine mesh resolution which dominates the total computational cost [20].…”

Section: Turbulence Simulationmentioning

confidence: 99%

“…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%

“…In [11,36,15] we show that approximate dissipative weak solutions can be computed to simulate turbulent flow using a stabilized finite element method that satisfies certain conditions on stability and consistency, which we refer to as a General Galerkin (G2) method. We also refer to the computational methodology as DFS, as an extension to turbulent flow of the general framework for a posteriori error estimation developed in the early 1990s [6][7][8].…”

Section: Direct Finite Element Simulationmentioning

confidence: 99%

“…A general framework for a posteriori error estimation based on duality for differential equations was developed in the 1990s described, e.g., in [6][7][8] and the references therein. Our own work has been focused on the extension of this framework to CFD and turbulent flow [9][10][11]. The method is validated for a range of basic benchmark problems including flow past cylinders, spheres and squares [12][13][14][15], where the adaptive algorithm is shown to converge to the experimental reference data.…”

Section: Introductionmentioning

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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Section: Turbulence Simulationmentioning

confidence: 99%

Section: Medium Reynolds Number Flowmentioning

confidence: 99%

Section: Direct Finite Element Simulationmentioning

confidence: 99%

Section: Introductionmentioning

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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“…In particular, the subgrid scale stabilization methods (also known as variational multiscale stabilization methods) [31,32] are of special interest for the simulation of turbulent flows. This is so because, if well designed, they not only allow one to circumvent the above mentioned numerical problems, but also act as implicit large eddy simulation models [32,33,34,35,36]. The basic idea of subgrid scale methods is that of splitting the problem unknowns, u 0 and p 0 for (15), and the test functions, v 0 and q 0 , into large scale components, u 0 h and p 0 h , which can be resolved by the computational mesh, and small scale components,ũ 0 andp 0 , which cannot be captured and whose effects onto the large scales have to be modeled.…”

Section: Spatial Discretizationmentioning

confidence: 99%

Concurrent finite element simulation of quadrupolar and dipolar flow noise in low Mach number aeroacoustics

et al. 2016

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The computation of flow-induced noise at low Mach numbers usually relies on a two-step hybrid methodolgy. In the first step, an incompressible fuid dynamics simulation (CFD) is performed and an acoustic source term is derived from it. The latter becomes the inhomegenous term for an acoustic wave equation, which is solved in the second step, often resorting to boundary integral formulations. In the presence of rigid bodies, Curle's acoustic analogy is probably the most extended approach. It has been shown that Curle's boundary dipolar noise contribution does in fact correspond to the diffraction of the quadrupolar aerodynamic noise generated by the flow past the rigid body. In this work, advantage is taken from this fact to propose an alternative computational methodology to get the individual quadrupolar and dipolar contributions to the total acoustic pressure. For any linear acoustic wave operator, the unknown acoustic pressure can be split into its incident and diffracted components and be computed simultaneously to the incompressible flow field, in a single finite element computational run. This circumvents the problem found in Curle's analogy of needing the total pressure at the body's boundary, which includes the acoustic pressure fluctuations. The latter cannot be obtained from an incompressible CFD simulation. The proposed unified strategy could be beneficial for a large variety problems such as those involving noise generated from duct terminations, or those related with the simulation of fricatives in numerical voice production, among many others.

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Computability and Adaptivity inCFD

Hoffman¹,

Johnson

2004

Encyclopedia of Computational Mechanics

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method constitutes a general flexible methodology for the discretization of the incompressible and compressible Navier-Stokes equations applicable to a great variety of flow problems from creeping viscous flow to slightly viscous flow, including free or moving boundaries. With continuous piecewise polynomials in space of order) and discontinuous or continuous Encyclopedia of Computational Mechanics.

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A new approach to computational turbulence modeling

Cited by 94 publications

References 8 publications

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

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

Concurrent finite element simulation of quadrupolar and dipolar flow noise in low Mach number aeroacoustics

Computability and Adaptivity inCFD

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