A particle-grid superposition method for the Navier-Stokes equations

Lee, Min Eig; Hariharan, S. I.; Ida, Nathan

doi:10.1016/0021-9991(90)90146-r

Cited by 30 publications

(24 citation statements)

References 8 publications

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“…Matching subdomains impose strong geometrical constraints on the grids defined on each sub-domain. By contrast, the flexibility added by overlapping sub-domains has already been useful to derive domain decomposition algorithms that combine Eulerian and Lagrangian solvers [3,15].…”

Section: Variable Blobs Local Mappings and Domain Decompositionmentioning

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: Variable Blobs Local Mappings and Domain Decompositionmentioning

confidence: 99%

“…• Particles x 1 p and x 2 p lying in 1 ∩ 3 and 2 ∩ 3 , respectively, are remeshed on the uniform mesh 3 ; we thus obtain a new distributionω 3 …”

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Vortex Methods with Spatially Varying Cores

Cottet

Koumoutsakos

Salihi

2000

Journal of Computational Physics

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“…As for the particle method, since the values of the weights are not affected by the convection, the mechanism for such an acceleration of the dissipation must involve the deformation of the Lagrangian mesh appearing in the diffusion formula (1.6). Actually, it can be observed that this deformation eventually leads to a local value of the viscosity which can exceed v significantly (see [2] for a discussion of this point). We have performed experiments with smooth and nonsmooth forcing terms.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

Large-Time Behavior of Deterministic Particle Approximations to the Navier-Stokes Equations

Cottet¹

1991

Mathematics of Computation

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“…A large number of the solvers, coming from the tremendous progress in the domain decomposition methods (see [30,31,38,43]), can be explored and possibly applied to problems set on unbounded domains. Currently, not much work achieved on the Schwarz algorithm for exterior problems has provided encouraging results (see, for instance, [2,9,32,33]). The core of this contribution is the new iterative method introduced in [3], for the Poisson model set in open domains, for which a full analysis is detailed.…”

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On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems

Belgacem

Fournié

Gmati³

et al. 2005

ESAIM: M2AN

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Abstract.Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence rate, an easy implementation, a substantial economy in computational costs and a satisfactory accuracy in the numerical results as well as their agreement with the theoretical statements.Mathematics Subject Classification. 35J20, 65N38, 65N55.

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A particle-grid superposition method for the Navier-Stokes equations

Cited by 30 publications

References 8 publications

Vortex Methods with Spatially Varying Cores

Vortex Methods with Spatially Varying Cores

Large-Time Behavior of Deterministic Particle Approximations to the Navier-Stokes Equations

On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems

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