On Spurious Vortical Structures

Drikakis, Dimitris; Smolarkiewicz, Piotr K.

doi:10.1006/jcph.2001.6825

Cited by 53 publications

(42 citation statements)

References 44 publications

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“…Here, two interpolation schemes have been employed: (a) the 'third-order' Lagrangian interpolator [6]; and (b) the MUSCL scheme [7]. For a comprehensive review of the listed schemes, see [8].…”

Section: Godunov-type Methodsmentioning

confidence: 99%

“…Using an explicit discretization in time while retaining a continuous representation in space, keeping track separately of the advective and advected velocities, and applying ∇ × to the resulting idealized algorithm leads to the vorticity equation (cf. [8])…”

Section: Vorticity Argument and Numerical Modificationsmentioning

confidence: 96%

“…Favourable cancellations can e ectively reduce the amplitude of the forcing at the second order, as is illustrated by our results summarized in the preceding section. For simple algorithms such as standard centred di erences, it is feasible to derive the ÿnite-di erence vorticity equation implied by the discrete momentum equation, and to reveal the explicit form of the rhs of (8). In the case of complicated algorithms like Godunov-or NFT-type methods this seems a hopeless task.…”

Section: Vorticity Argument and Numerical Modificationsmentioning

confidence: 98%

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On ‘spurious’ eddies

Drikakis

Margolin

Smolarkiewicz

2002

Numerical Methods in Fluids

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SUMMARYRecently, several papers have appeared in the CFD literature, proposing an idealized instability problem as a benchmark for discriminating among numerical algorithms for two-dimensional Navier-Stokes ows. The problem is a double shear layer simulated at coarse resolution and with a prescribed interface perturbation. A variety of second-order accurate schemes have been tested, with all results falling into one of two solution patterns-one pattern with two eddies and the other with three eddies. In the literature, there is no fast-and-ÿrm rule to predict the results of any particular algorithm. However, it is asserted that the two-eddy solution is correct. Our own research has led to two conclusions. First, the appearance of the third eddy is tied up with small details of the truncation error; we illustrate this point by prescribing small changes that lead to reversal of the appearance=disappearance of the third eddy in several schemes. Second, we discuss the realizability of the two solutions and suggest that the three-eddy solution is the more physical. Overall, we conclude that this problem is a poor choice of benchmark to discriminate among numerical algorithms.

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Section: Godunov-type Methodsmentioning

confidence: 99%

Section: Vorticity Argument and Numerical Modificationsmentioning

confidence: 96%

Section: Vorticity Argument and Numerical Modificationsmentioning

confidence: 98%

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On ‘spurious’ eddies

Drikakis

Margolin

Smolarkiewicz

2002

Numerical Methods in Fluids

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“…[34][35][36] Finally, the calculated maximum error of the relative effective viscosity 37 eff (t) = (t) (t) to the physical viscosity , where is the dissipation rate Equation 24 and is the enstrophy Equation 25.…”

Section: Figure 10mentioning

confidence: 99%

Three‐dimensional remeshed smoothed particle hydrodynamics for the simulation of isotropic turbulence

Obeidat

Bordas

2017

Numerical Methods in Fluids

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SummaryWe present a remeshed particle-mesh method for the simulation of three-dimensional compressible turbulent flow. The method is related to the meshfree smoothed particle hydrodynamics method, but the present method introduces a mesh for efficient calculation of the pressure gradient, and laminar and turbulent diffusion. In addition, the mesh is used to remesh (reorganise uniformly) the particles to ensure a regular particle distribution and convergence of the method. The accuracy of the presented methodology is tested for a number of benchmark problems involving two-and three-dimensional Taylor-Green flow, thin double shear layer, and three-dimensional isotropic turbulence. Two models were implemented, direct numerical simulations, and Smagorinsky model. Taking advantage of the Lagrangian advection, and the finite difference efficiency, the method is capable of providing quality simulations while maintaining its robustness and versatility.

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“…Are they non-physical vortices that appear as solutions of a turbulence model used that do not reflect appropriate averages of the true flow's eddies? Studies of the second question have been pioneered by Brown and Minon [2] and Drikakis and Smolarkiewicz [4]. Our aim here is to begin considering the third question in an (admittedly quite simplified) setting which admits analytical attack.…”

mentioning

confidence: 99%

On a well-posed turbulence model

Layton

Lewandowski

2006

Discrete &Amp; Continuous Dynamical Systems - B

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Abstract. This report considers mathematical properties, important for practical computations, of a model for the simulation of the motion of large eddies in a turbulent flow. In this model, closure is accomplished in the very simple way:uu ∼ūū, yielding the modelIn particular, we prove existence and uniqueness of strong solutions, develop the regularity of solutions of the model and give a rigorous bound on the modelling error, ||ū − w||. Finally, we consider the question of non-physical vortices (false eddies), proving that the model correctly predicts that only a small amount of vorticity results when the total turning forces on the flow are small. 1.Introduction. The great challenge in simulation of turbulent flows from applications ranging from geophysics to biomedical device design is that equations for the pointwise flow quantities are well-known but intractable to computational solution and sensitive to uncertainties and perturbation in problem data. On the other hand, closed equations for the averages of flow quantities cannot be obtained directly from the physics of fluid motion. Thus, modeling in large eddy simulation (meaning the approximation of local, spacial averages in a turbulent flow) is typically based on guesswork (phenomenology), calibration (data fitting model parameters) and (at best) approximation.

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On Spurious Vortical Structures

Cited by 53 publications

References 44 publications

On ‘spurious’ eddies

On ‘spurious’ eddies

Three‐dimensional remeshed smoothed particle hydrodynamics for the simulation of isotropic turbulence

On a well-posed turbulence model

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