A General Deterministic Treatment of Derivatives in Particle Methods

Eldredge, Jeff D.; Leonard, Anthony; Colonius, Tim

doi:10.1006/jcph.2002.7112

Cited by 118 publications

(133 citation statements)

References 17 publications

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“…The second term is the viscous diffusion term, which can be solved using the particle strength exchange technique (Eldredge, Leonard, & Colonius, 2002). In actuality, only a subset Q p of all the particles needs to be considered when integrating over the volume V p of particle p; the viscous diffusion term can be written as…”

Section: Rotor-wake Dynamics Modelmentioning

confidence: 99%

Rotor wake and flow analysis using a coupled Eulerian–Lagrangian method

Shi

Peng

2016

Engineering Applications of Computational Fluid Mechanics

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A coupled Eulerian-Lagrangian methodology was developed in this paper in order to provide an efficient and accurate tool for rotor wake and flow prediction. A Eulerian-based Reynolds-averaged Navier-Stokes (RANS) solver was employed to simulate the grid-covered near-body zone, and a gridfree Lagrangian-based viscous wake method (VWM) was implemented to model the complicated rotor-wake dynamics in the off-body wake zone. A carefully designed coupling strategy was developed to pass the flow variables between two solvers. A sample case of a forward flying rotor was performed first in order to show the capabilities of the VWM for wake simulations. Next, the coupled method was applied to rotors in several representative flight conditions. Excellent agreement regarding wake geometry, chordwise pressure distribution and sectional normal force with available experimental data demonstrated the validity of the method. In addition, a comparison with the full computational fluid dynamics (CFD) method is presented to illustrate the efficiency and accuracy of the proposed coupled method. ARTICLE HISTORY

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Section: Rotor-wake Dynamics Modelmentioning

confidence: 99%

Rotor wake and flow analysis using a coupled Eulerian–Lagrangian method

Shi

Peng

2016

Engineering Applications of Computational Fluid Mechanics

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“…Thus the local speed of sound satisfies a 2 = (γ − 1)h, where γ is the ratio of specific heats (taken to be 1.4). The spatial derivatives in equations (4)- (8) (for all except the velocity) are discretized using PSE [10], extendable to general differential operators as shown by Eldredge et al [11]. The essence of the method is the approximation of the derivative D β (where β is a multi-index denoting the degree of derivative) by the operator,…”

Section: Equations Of Motionmentioning

confidence: 99%

“…on the enthalpy in a circular boundary zone of a few particles' depth at r = R. The spatial derivative is approximated by a one-sided form of PSE to respect the boundary [11]. As in incompressible methods, occasional reinitialization of the particles is necessary for the long-term stability of the method.…”

Section: Other Aspectsmentioning

confidence: 99%

A dilating vortex particle method for compressible flow

Eldredge¹,

Colonius²,

Leonard³

2002

Journal of Turbulence

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Abstract. Vortex methods have become useful tools for the computation of incompressible fluid flow. In this work, a vortex particle method for the simulation of unsteady two-dimensional compressible flow is developed. By decomposing the velocity into irrotational and solenoidal parts, and using particles that are able to change volume and that carry vorticity, dilatation, enthalpy, entropy and density, the equations of motion are satisfied. Spatial derivatives are treated using the method of particle strength exchange with highorder-accurate, non-dissipative kernels. The new vortex method is applied to co-rotating and leapfrogging vortices in compressible flow, with the far acoustic field computed using a two-dimensional Kirchhoff surface.

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“…These include the deterministic method for the treatment of diffusion developed by Degond and Mas-Gallic [12], now referred to as particle strength exchange (PSE). As we show in [14], PSE also furnishes a useful framework for treating other physical phenomena, such as wave propagation. The expensive summation operation that once prohibited simulations of particle systems involving more than a few thousand particles has been alleviated with the development of fast methods, such as the fast multipole method of Greengard and Rokhlin [21].…”

Section: Introductionmentioning

confidence: 98%

“…Computational elements that expand and contract according to the dilatation are introduced in this section, as well as a set of equations governing their strengths based on the compressible equations of motion. Domain truncation is dealt with in Section 3; a scheme based on Engquist and Majda's local boundary conditions [15] is described using the one-sided derivative treatment developed in [14]. In Section 4 other points for practical implementation are discussed, including the adaptations of the fast summation method and particle remeshing.…”

Section: Introductionmentioning

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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A General Deterministic Treatment of Derivatives in Particle Methods

Cited by 118 publications

References 17 publications

Rotor wake and flow analysis using a coupled Eulerian–Lagrangian method

Rotor wake and flow analysis using a coupled Eulerian–Lagrangian method

A dilating vortex particle method for compressible flow

A Vortex Particle Method for Two-Dimensional Compressible Flow

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