Accuracy considerations for implementing velocity boundary condiditons in vorticity formulations

Kempka, S.N.; Glass, Michael; Peery, J.S.; Strickland, J. H.; Ingber,

doi:10.2172/242701

Cited by 41 publications

(49 citation statements)

References 6 publications

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“…In the present formulation, determining both the interior velocity ÿeld and the creation of vorticity on the boundary are accomplished in a uniÿed manner using the GHD. A complete derivation of the GHD is presented by Kempka [14].…”

Section: Mathematical and Numerical Formulationmentioning

confidence: 99%

Parallel multipole implementation of the generalized Helmholtz decomposition for solving viscous flow problems

Brown

Mammoli

Ingber

2003

Numerical Meth Engineering

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SUMMARYThe evaluation of a domain integral is the dominant bottleneck in the numerical solution of viscous ow problems by vorticity methods, which otherwise demonstrate distinct advantages over primitive variable methods. By applying a Barnes-Hut multipole acceleration technique, the operation count for the integration is reduced from O(N 2 ) to O(N log N ), while the memory requirements are reduced from O(N 2 ) to O(N ). The algorithmic parameters that are necessary to achieve such scaling are described. The parallelization of the algorithm is crucial if the method is to be applied to realistic problems. A parallelization procedure which achieves almost perfect scaling is shown. Finally, numerical experiments on a driven cavity benchmark problem are performed. The actual increase in performance and reduction in storage requirements match theoretical predictions well, and the scalability of the procedure is very good.

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Section: Mathematical and Numerical Formulationmentioning

confidence: 99%

Parallel multipole implementation of the generalized Helmholtz decomposition for solving viscous flow problems

Brown

Mammoli

Ingber

2003

Numerical Meth Engineering

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“…For ÿeld points x on the boundary, Equation (2) can be augmented to allow for a slip velocity by including the vortex sheet of strength S as follows [30]:…”

Section: Mathematical Formulationmentioning

confidence: 99%

Parallelization of a vorticity formulation for the analysis of incompressible viscous fluid flows

Brown

Ingber

2002

Numerical Methods in Fluids

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SUMMARYA parallel computer implementation of a vorticity formulation for the analysis of incompressible viscous uid ow problems is presented. The vorticity formulation involves a three-step process, two kinematic steps followed by a kinetic step. The ÿrst kinematic step determines vortex sheet strengths along the boundary of the domain from a Galerkin implementation of the generalized Helmholtz decomposition. The vortex sheet strengths are related to the vorticity ux boundary conditions. The second kinematic step determines the interior velocity ÿeld from the regular form of the generalized Helmholtz decomposition. The third kinetic step solves the vorticity equation using a Galerkin ÿnite element method with boundary conditions determined in the ÿrst step and velocities determined in the second step. The accuracy of the numerical algorithm is demonstrated through the driven-cavity problem and the 2-D cylinder in a free-stream problem, which represent both internal and external ows. Each of the three steps requires a unique parallelization e ort, which are evaluated in terms of parallel e ciency.

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“…It is interesting to note that none of these investigators reference one another except Morino who briefly notes some of Wu's work. A complete derivation of the GHD can be found in Kempka et al [11]. The GHD for an incompressible fluid in two dimensions is given by…”

Section: Mathematical Formulationmentioning

confidence: 99%

A Galerkin Implementation of the Generalized Helmholtz Decomposition for Vorticity Formulations

Ingber

Kempka²

2001

Journal of Computational Physics

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Accuracy considerations for implementing velocity boundary condiditons in vorticity formulations

Cited by 41 publications

References 6 publications

Parallel multipole implementation of the generalized Helmholtz decomposition for solving viscous flow problems

Parallel multipole implementation of the generalized Helmholtz decomposition for solving viscous flow problems

Parallelization of a vorticity formulation for the analysis of incompressible viscous fluid flows

A Galerkin Implementation of the Generalized Helmholtz Decomposition for Vorticity Formulations

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