Boundary Conditions for Viscous Vortex Methods

Koumoutsakos, Petros; Leonard, Anthony; Pepin, F.

doi:10.1006/jcph.1994.1117

Cited by 133 publications

(128 citation statements)

References 2 publications

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“…This has been used as the basis for a numerical algorithm with vortex particle methods (e.g. [12,19,20]) and a Cartesian grid method [21]. For the purposes of the present paper, we can regard each timestep as split into two subseps: in the first, fluid vorticity evolves by convection and the body evolves by its own dynamics, but their independent evolution leaves a spurious slip velocity on the body surface; this slip is then annihilated in the second substep by diffusing the vortex sheet into the fluid (while the fluid and body remain stationary).…”

Section: Methodsmentioning

confidence: 99%

“…For the purposes of the present paper, we can regard each timestep as split into two subseps: in the first, fluid vorticity evolves by convection and the body evolves by its own dynamics, but their independent evolution leaves a spurious slip velocity on the body surface; this slip is then annihilated in the second substep by diffusing the vortex sheet into the fluid (while the fluid and body remain stationary). The vortex sheet is introduced into the fluid by solving a linear diffusion problem with the Neumann boundary condition ν∂ω/∂n = −γ / t, where ν is the kinematic viscosity, γ is the strength of the vortex sheet associated with spurious slip, and t is the (vanishingly-small) time interval over which the sheet is diffused [19].…”

Section: Methodsmentioning

confidence: 99%

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A Reconciliation of Viscous and Inviscid Approaches to Computing Locomotion of Deforming Bodies

Eldredge

2009

Exp Mech

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We present a formulation for coupled solutions of fluid and body dynamics in problems of biolocomotion. This formulation unifies the treatment at moderate to high Reynolds number with the corresponding inviscid problem. By a viscous splitting of the Navier-Stokes equations, inertial forces from the fluid are distinguished from the viscous forces, and the former are further decomposed into contributions from body motion in irrotational fluid and ambient fluid vorticity about an equivalent stationary body. In particular, the added mass of the fluid is combined with the intrinsic inertia of the body to allow for simulations of bodies of arbitrary mass, including massless or neutrally buoyant bodies. The resulting dynamical equations can potentially illuminate the role of vorticity in locomotion, and the fundamental differences of locomotion in real and perfect fluids.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

A Reconciliation of Viscous and Inviscid Approaches to Computing Locomotion of Deforming Bodies

Eldredge

2009

Exp Mech

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“…Inhomogeneous and mixed boundary conditions can be enforced by locally modifying the intensities of the particles in the neighborhood of the boundary [24] or by treating them as artificial reaction terms [36].…”

Section: Boundary Conditionsmentioning

confidence: 99%

A self-organizing Lagrangian particle method for adaptive-resolution advection–diffusion simulations

Reboux

Schrader

Sbalzarini

2012

Journal of Computational Physics

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We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two-and three-dimensional benchmark problems. These include advection-diffusion, the Burgers equation, the Buckley-Leverett five-spot problem, and curvature-driven level-set surface refinement. AbstractWe present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two-and three-dimensional benchmark problems. These include advection-diffusion, the Burgers equation, the Buckley-Leverett five-spot problem, and curvature-driven level-set surface refinement.

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“…PSE is used for Laplacian terms, as well as for the first derivatives of enthalpy, entropy, dilatation, and vorticity, with separate kernels used for each order of derivative. It should be noted that (17) has been used with β = 2 (the Laplacian) extensively in vortex methods (see, e.g., [25,47]) and with β = 1 (the gradient) in, for example, SPH [34]. Quackenbush et al [41] used the β = 1 form to compute the gradient of the density, although their formula is not conservative.…”

Section: Equations Of Motionmentioning

confidence: 99%

A Vortex Particle Method for Two-Dimensional Compressible Flow

Eldredge

Colonius

Leonard

2002

Journal of Computational Physics

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A vortex particle method is developed for simulating two-dimensional, unsteady compressible flow. The method uses the Helmholtz decomposition of the velocity field to separately treat the irrotational and solenoidal portions of the flow, and the particles are allowed to change volume to conserve mass. In addition to having vorticity and dilatation properties, the particles also carry density, enthalpy, and entropy. The resulting evolution equations contain terms that are computed with techniques used in some incompressible methods. Truncation of unbounded domains via a nonreflecting boundary condition is also considered. The fast multipole method is adapted to compressible particles in order to make the method computationally efficient. The new method is applied to several problems, including sound generation by corotating vortices and generation of vorticity by baroclinic torque. c 2002 Elsevier Science (USA)

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Boundary Conditions for Viscous Vortex Methods

Cited by 133 publications

References 2 publications

A Reconciliation of Viscous and Inviscid Approaches to Computing Locomotion of Deforming Bodies

A Reconciliation of Viscous and Inviscid Approaches to Computing Locomotion of Deforming Bodies

A self-organizing Lagrangian particle method for adaptive-resolution advection–diffusion simulations

A Vortex Particle Method for Two-Dimensional Compressible Flow

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