Multi-purpose regridding in vortex methods

Cottet, Georges-Henri; Salihi, Mohamed Lemine Ould; Hamroui, M. El

doi:10.1051/proc:1999009

Cited by 18 publications

(22 citation statements)

References 6 publications

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“…The regularization implied in this formula is motivated by the fact that the particle representation (6) would lead to singular evaluations of the velocity in (5). For a thorough discussion of the point and smooth vortex methods and their numerical analysis we refer to [4] and the references therein.…”

Section: Governing Equations and Vortex Methodsmentioning

confidence: 99%

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Vortex Methods with Spatially Varying Cores

Cottet

Koumoutsakos

Salihi

2000

Journal of Computational Physics

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The accuracy of vortex methods employing smooth vortex particles/blobs is determined by the blob size, which can be viewed as a mollifier of the vorticity field. For computational efficiency, this core size needs to be spatially variable as particles are used to discretize different parts of the flow field, such as the boundary layer and the wake in bluff body flows. We derive here a consistent approximation for the viscous Navier-Stokes equations using variable size vortex particles. This derivation is based on the implementation of mappings that allow the consistent formulation of the diffusion and convection operators of the Navier-Stokes equations in the context of vortex methods. Several local mappings can be combined giving the capability of "mesh-embedding" to vortex methods. It is shown that the proposed variable method offers a significant improvement on the computational efficiency of constant core size methods while maintaining the adaptive character of the method. The method is ideally suited to flows such as wakes and shear layers and the validity of the approach is illustrated by showing results from cylinder flows and wall-vortex interactions. Using this scheme, previously unattainable simulations of cylinders undergoing rotary oscillations at high Reynolds numbers reveal an interesting mechanism for drastic drag reduction.

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Section: Governing Equations and Vortex Methodsmentioning

confidence: 99%

“…This is not a drastic constraint: in a vortex code, the time-step is typically scaled by the inverse of the maximum vorticity, and remeshing at every time step with a third or fourth interpolation formula introduces only a marginal numerical discrepancy [5,12].…”

Section: Remeshing For Variable Size Blobsmentioning

confidence: 99%

Vortex Methods with Spatially Varying Cores

Cottet

Koumoutsakos

Salihi

2000

Journal of Computational Physics

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“…On the other hand, there are some problems with the vortex methods. Lagrangian description of the vortex particles' movement may make the particle distribution become uneven and destroy the overlapping conditions which necessitates a remeshing process [19]. The vorticity boundary conditions are di cult to deal with although some e orts have been made [11,20].…”

Section: Introductionmentioning

confidence: 99%

Finite volume solution of the Navier-Stokes equations in velocity-vorticity formulation

Zhu

2005

Int. J. Numer. Meth. Fluids

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SUMMARYFor the incompressible Navier-Stokes equations, vorticity-based formulations have many attractive features over primitive-variable velocity-pressure formulations. However, some features interfere with the use of the numerical methods based on the vorticity formulations, one of them being the lack of a boundary conditions on vorticity. In this paper, a novel approach is presented to solve the velocityvorticity integro-di erential formulations. The general numerical method is based on standard ÿnite volume scheme. The velocities needed at the vertexes of each control volume are calculated by a socalled generalized Biot-Savart formula combined with a fast summation algorithm, which makes the velocity boundary conditions implicitly satisÿed by maintaining the kinematic compatibility of the velocity and vorticity ÿelds. The well-known fractional step approaches are used to solve the vorticity transport equation. The paper describes in detail how we accurately impose no normal-ow and no tangential-ow boundary conditions. We impose a no-ux boundary condition on solid objects by the introduction of a proper amount of vorticity at wall. The di usion term in the transport equation is treated implicitly using a conservative ÿnite update. The di usive uxes of vorticity into ow domain from solid boundaries are determined by an iterative process in order to satisfy the no tangential-ow boundary condition. As application examples, the impulsively started ows through a at plate and a circular cylinder are computed using the method. The present results are compared with the analytical solution and other numerical results and show good agreement.

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“…Here, we use a bi-linear interpolation so G ij only consists of four grid boxes. But we also tested a third order interpolation scheme, namely the third-order interpolation scheme M ′ 4 of Cottet et al (1999), using 16 points and in this case G ij consists of 16 grid boxes. Third-order schemes are known to be more accurate and are commonly used in VIC methods (the M ′ 4 scheme is used with the VIC algorithm in §3).…”

Section: Transfer Of a Gridded Field To Point Vorticesmentioning

confidence: 99%