A fast 3D particle method for the simulation of buoyant flow

Schlegel, Fabrice; Wee, Daehyun; Ghoniem, Ahmed F.

doi:10.1016/j.jcp.2008.03.036

Cited by 13 publications

(7 citation statements)

References 34 publications

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“…The elongated tail of the vortex ring, captured at much finer resolutions in [16,17,18,20], is also reproduced in Case II, while Case I truncates this subtle feature.…”

Section: Evolution Of a Vortex Ringmentioning

confidence: 78%

“…The ring's core radius is chosen to be a/R = 0.35. This set of parameters makes the initial condition identical to that of a previous axisymmetric spectral simulation reported in [17,18] and to that of other vortex calculations reported in [16,20]. The initial condition is discretized on a relatively fine grid whose mesh size is Δx = 0.025.…”

Section: Evolution Of a Vortex Ringmentioning

confidence: 99%

“…The numerical discretization of the equation of motion closely follows that of [16]. A second-order predictor/corrector scheme is used for evaluating advection.…”

Section: Evolution Of a Vortex Ringmentioning

confidence: 99%

“…Parallelization is done in a similar way to that discussed in [12]. The results are reported in the following dimensionless variables, which were also used in previous related works [16,17,18,20]. The dimensionless speed of the vortex ring centroid is given by…”

Section: Evolution Of a Vortex Ringmentioning

confidence: 99%

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Convergence Characteristics and Computational Cost of Two Algebraic Kernels in Vortex Methods with a Tree-Code Algorithm

Wee¹,

Marzouk²,

Schlegel³

et al. 2009

SIAM J. Sci. Comput.

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Abstract. We study the convergence characteristics of two algebraic kernels used in vortex calculations: the Rosenhead-Moore kernel, which is a low-order kernel, and the Winckelmans-Leonard kernel, which is a high-order kernel. To facilitate the study, a method of evaluating particle-cluster interactions is introduced for the Winckelmans-Leonard kernel. The method is based on Taylor series expansion in Cartesian coordinates, as initially proposed by Lindsay and Krasny [J. Comput. Phys., 172 (2001), pp. 879-907] for the Rosenhead-Moore kernel. A recurrence relation for the Taylor coefficients of the Winckelmans-Leonard kernel is derived by separating the kernel into two parts, and an error estimate is obtained to ensure adaptive error control. The recurrence relation is incorporated into a tree-code to evaluate vorticity-induced velocity. Next, comparison of convergence is made while utilizing the tree-code. Both algebraic kernels lead to convergence, but the Winckelmans-Leonard kernel exhibits a superior convergence rate. The combined desingularization and discretization error from the Winckelmans-Leonard kernel is an order of magnitude smaller than that from the Rosenhead-Moore kernel at a typical resolution. Simulations of vortex rings are performed using the two algebraic kernels in order to compare their performance in a practical setting. In particular, numerical simulations of the side-by-side collision of two identical vortex rings suggest that the three-dimensional evolution of vorticity at finite resolution can be greatly affected by the choice of the kernel. We find that the Winckelmans-Leonard kernel is able to perform the same task with a much smaller number of vortex elements than the Rosenhead-Moore kernel, greatly reducing the overall computational cost.

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“…The elongated tail of the vortex ring, captured at much finer resolutions in [16,17,18,20], is also reproduced in Case II, while Case I truncates this subtle feature.…”

Section: Evolution Of a Vortex Ringmentioning

confidence: 78%

Section: Evolution Of a Vortex Ringmentioning

confidence: 99%

“…The numerical discretization of the equation of motion closely follows that of [16]. A second-order predictor/corrector scheme is used for evaluating advection.…”

Section: Evolution Of a Vortex Ringmentioning

confidence: 99%

Section: Evolution Of a Vortex Ringmentioning

confidence: 99%

See 2 more Smart Citations

Convergence Characteristics and Computational Cost of Two Algebraic Kernels in Vortex Methods with a Tree-Code Algorithm

Wee¹,

Marzouk²,

Schlegel³

et al. 2009

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…Such flows have been known to be handled effectively by vortex methods, and several recent applications of high-quality vortex methods have focused on vortex rings [6][7][8]. Vortex methods solve the NavierStokes equation in the velocity-vorticity form with Lagrangian discretization.…”

Section: Introductionmentioning

confidence: 99%

Comparing the treecode with FMM on GPUs for vortex particle simulations of a leapfrogging vortex ring

Yokota

Barba

2011

Computers & Fluids

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Simulation of a high Reynolds number reactive transverse jet and the formation of a triple flame

Schlegel

Ghoniem

2014

Combustion and Flame

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A fast 3D particle method for the simulation of buoyant flow

Cited by 13 publications

References 34 publications

Convergence Characteristics and Computational Cost of Two Algebraic Kernels in Vortex Methods with a Tree-Code Algorithm

Convergence Characteristics and Computational Cost of Two Algebraic Kernels in Vortex Methods with a Tree-Code Algorithm

Comparing the treecode with FMM on GPUs for vortex particle simulations of a leapfrogging vortex ring

Simulation of a high Reynolds number reactive transverse jet and the formation of a triple flame

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