The normal and oblique collision of a dipole with a no-slip boundary

Clercx, Hjh Herman; Bruneau, Charles‐Henri

doi:10.1016/j.compfluid.2004.11.009

Cited by 76 publications

(111 citation statements)

References 20 publications

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“…Extensions of the present work will consider the true nature of the boundary condition in the volume penalisation method, non-normal incidence collisions which may be benchmarked against Clercx and Bruneau, 18 and extending the compact finite difference method to circular domains.…”

Section: Discussionmentioning

confidence: 99%

The effect of slip length on vortex rebound from a rigid boundary

2013

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The problem of a dipole incident normally on a rigid boundary, for moderate to large Reynolds numbers, has recently been treated numerically using a volume penalisation method by Nguyen van yen, Farge, and Schneider [Phys. Rev. Lett. 106, 184502 (2011)]. Their results indicate that energy dissipating structures persist in the inviscid limit. They found that the use of penalisation methods intrinsically introduces some slip at the boundary wall, where the slip approaches zero as the Reynolds number goes to infinity, so reducing to the no-slip case in this limit. We study the same problem, for both no-slip and partial slip cases, using compact differences on a Chebyshev grid in the direction normal to the wall and Fourier methods in the direction along the wall. We find that for the no-slip case there is no indication of the persistence of energy dissipating structures in the limit as viscosity approaches zero and that this also holds for any fixed slip length. However, when the slip length is taken to vary inversely with Reynolds number then the results of Nguyen van yen et al. are regained. It therefore appears that the prediction that energy dissipating structures persist in the inviscid limit follows from the two limits of wall slip length going to zero, and viscosity going to zero, not being treated independently in their use of the volume penalisation method.

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Section: Discussionmentioning

confidence: 99%

The effect of slip length on vortex rebound from a rigid boundary

2013

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“…Section 3.3 discusses the initialization and execution of the code in parallel, including pitfalls related to analysis that needs global quantities. Section 3.4 replicates the work of Clercx and Bruneau [2006] and to look at the interaction of a translating dipole with a no-slip boundary, and section 3.5 discusses the spectral filtering algorithms used to help ensue stability in under-resolved simulations. Finally, section 3.6 demonstrates internal wave generation over topography, using a coordinate-mapped grid to include a large hill in the middle of the domain.…”

Section: Organization and Algorithm Overviewmentioning

confidence: 99%

“…To illustrate this, this section covers the code required to simulate the two-dimensional collision of a dipole with a no-slip boundary, repeating the case in Clercx and Bruneau [2006] presented as an appropriate test case for simulation codes.…”

Section: The Translating Dipole and Boundary Interactionmentioning

confidence: 99%

“…This section follows Clercx and Bruneau [2006] in normalizing the initial kinetic energy (0.5 u 2 + w 2 dV ) to 2, which coincidentally gives a root-mean-squared velocity of 1. This RMS velocity is used with the domain half-width (1) to define the Reynolds' number for the simulation.…”

Section: The Translating Dipole and Boundary Interactionmentioning

confidence: 99%

“…Comparison with Clercx and Bruneau [2006] and require computation of kinetic energy and enstrophy 18 , along with periodic views of the vorticity field. The first two require volume integration and ideally should be computed at each timestep, and the latter two require computation of the vorticity.…”

Section: Analysis and The Gradient Operatormentioning

confidence: 99%

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Simulation of the Navier–Stokes equations in three dimensions with a spectral collocation method

Subich

Lamb

Stastna

2013

Numerical Methods in Fluids

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SUMMARYThis paper describes a nonlinear, three‐dimensional spectral collocation method for the simulation of the incompressible Navier–Stokes equations under the Boussinesq approximation, motivated by geophysical and environmental flows. These flows are driven by the interaction of stratified fluid with topography, which this model accurately accounts for by using a mapped coordinate system. The spectral collocation method is implemented with both a Fourier trigonometric expansion and the Chebyshev polynomials, as appropriate for the domain boundary conditions. The coordinate mapping prohibits the use of existing, fast solution methods that rely on the separation of variables, so a preconditioner based on the approximate solution of a corresponding finite‐difference problem with geometric multigrid is used. The model is parallelized with the Message Passing Interface library, and it runs effectively on shared and distributed‐memory systems. Copyright © 2013 John Wiley & Sons, Ltd.

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Study of a staggered fourth‐order compact scheme for unsteady incompressible viscous flows

Knikker

2008

Numerical Methods in Fluids

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SUMMARYThe objective of this paper is the development and assessment of a fourth-order compact scheme for unsteady incompressible viscous flows. A brief review of the main developments of compact and highorder schemes for incompressible flows is given. A numerical method is then presented for the simulation of unsteady incompressible flows based on fourth-order compact discretization with physical boundary conditions implemented directly into the scheme. The equations are discretized on a staggered Cartesian non-uniform grid and preserve a form of kinetic energy in the inviscid limit when a skew-symmetric form of the convective terms is used.The accuracy and efficiency of the method are demonstrated in several inviscid and viscous flow problems. Results obtained with different combinations of second-and fourth-order spatial discretizations and together with either the skew-symmetric or divergence form of the convective term are compared. The performance of these schemes is further demonstrated by two challenging flow problems, linear instability in plane channel flow and a two-dimensional dipole-wall interaction. Results show that the compact scheme is efficient and that the divergence and skew-symmetric forms of the convective terms produce very similar results. In some but not all cases, a gain in accuracy and computational time is obtained with a high-order discretization of only the convective and diffusive terms. Finally, the benefits of compact schemes with respect to second-order schemes is discussed in the case of the fully developed turbulent channel flow.

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The normal and oblique collision of a dipole with a no-slip boundary

Cited by 76 publications

References 20 publications

The effect of slip length on vortex rebound from a rigid boundary

The effect of slip length on vortex rebound from a rigid boundary

Simulation of the Navier–Stokes equations in three dimensions with a spectral collocation method

Study of a staggered fourth‐order compact scheme for unsteady incompressible viscous flows

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