Fundamental solutions and numerical methods for flow problems

Wu, J. C.

doi:10.1002/fld.1650040207

Cited by 38 publications

(13 citation statements)

References 11 publications

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“…In Ref. (165), it has been shown that the solid boundary vorticity values can be determined through the kinematic relationship between the instantaneous velocity and vorticity fields. It should be noted that the kinematic relationship, Equation (B2), is valid in both the solid region S and the fluid region R. Therefore, the vorticity field throughout S and R must be such that the velocity in S as computed by Equation (B2) should agree with the prescribed solid body motion.…”

Section: B1 Velocity-vorticity Formulationmentioning

confidence: 99%

Computational prediction of airfoil dynamic stall

Ekaterinaris

Platzer

1998

Progress in Aerospace Sciences

291

127

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Section: B1 Velocity-vorticity Formulationmentioning

confidence: 99%

Computational prediction of airfoil dynamic stall

Ekaterinaris

Platzer

1998

Progress in Aerospace Sciences

291

127

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“…(1) and (2). Detailed numerical procedures are described in Sohn (1986), who developed a numerical method of solving the time-dependent incompressible Navier-Stokes equations in the integro-differential formulation based on Wu (1984). The reliability and accuracy of the numerical method has been ascertained.…”

Section: Boundary Conditions and Discretization Of The Governing Equamentioning

confidence: 99%

Numerical flow visualization of first cycle and cyclic motion of a rigid fling-clapping wing

Chang

Sohn

2006

J Vis

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A flow visualization of the two-dimensional rigid fling-clap motions of the flat-plate wing is performed to get the knowledge of fling-clapping mechanism that might be employed by insects during flight. In this numerical visualization, the time-dependent Navier-Stokes equations are solved for two types of wing motion; 'fling followed by clap and pause motion' and 'cyclic fling-clapping motion'. The result is observed regarding the main flow features such as the sequential development of the two families of separation vortex pairs and their movement. For the 'fling followed by clap and pause motion', a strong separation vortex pair of counterrotation develops in the opening between the wings in the fling phase and they then move out from the opening in the following clap phase. For 'the cyclic fling-clapping motion', the separation vortex pair developed in the outside space in the clap phase move into the opening in the following fling phase. The separation vortex pair in the opening developed in the fling phase of the cyclic motion is observed to be stronger than those of the 'fling followed by clap and pause motion'. Regarding the strong fling separation vortex and the weak clap separation vortex above it in the opening, the flow pattern of the fling phase of the cyclic fling and clap motion is different to that of the fling phase of the first cycle. The flow pattern of the third cycle of the cyclic fling-clapping motion is observed to be almost same as that of the second cycle. Therefore, a periodicity of the flow pattern is established after the second cycle.

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“…The velocity corrections which were obtained from BIE (25) may be analogously compared with the ones obtained from (7), where the pressure derivatives were determined by an alternative differencing (usually, velocity derivatives) of the pressure corrections from (23).…”

Section: Velocity Corrections As the Equalitymentioning

confidence: 99%

A boundary element formulation using the simple method

Grigor'ev¹

1993

Numerical Methods in Fluids

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SUMMARYA new boundary element method is described for calculation of the steady incompressible laminar flows. The method is based on the well-known SIMPLE algorithm. The new boundary element method allows one to find the fields of the pressure and velocity corrections without inner iterations, thus reducing the computational time drastically. This makes it different from the method developed by Patankar and S~alding.~' However, the new method demands a much larger computer storage. The boundary integral equations are discretized with the help of constant boundary elements and constant cells. The values of the integrals along the boundary elements and the cells for the two-dimensional domain are found analytically. To preserve the stability in the iteration process, under-relaxation for the convection terms is used. This paper gives the results of calculations of the flows between two plane parallel plates at Re = 20 and Re = 200, the flows in a square cavity with a moving upper lid at Re= 1 and Re= 100 and the flow in a plane channel with sudden symmetric expansion at Re = 46.6. KEY WORDS Boundary integral equation Boundary element method SIMPLE algorithm Two-dimensional laminar flow

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Fundamental solutions and numerical methods for flow problems

Cited by 38 publications

References 11 publications

Computational prediction of airfoil dynamic stall

Computational prediction of airfoil dynamic stall

Numerical flow visualization of first cycle and cyclic motion of a rigid fling-clapping wing

A boundary element formulation using the simple method

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