A hybrid finite-boundary element method for inviscid flows with free surface

Pelekasis, N.; Tsamopoulos, John; Manolis, George D.

doi:10.1016/0021-9991(92)90001-f

Cited by 26 publications

(31 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…18 In fact, it was seen that, for small initial deformations, doubling the number of elements along the interface required, roughly, a four times smaller time step for numerical stability. Solution of the unknowns of the problem is done sequentially.…”

Section: Numerical Solutionmentioning

confidence: 98%

“…In the present study the effect of initial elongation has to be accounted for as well. In practice, in order to respect the stability requirements of the Runge-Kutta time integrator which were found elsewhere 18 to obey a quadratic law, ⌬t ϳ ⌬s min 2 , and to account for the decreasing radius of curvature as parameter S decreases, in the simulations to be presented hereafter the time step was initially set to ⌬t = ⌬s min 2 S. This scaling was found to be appropriate in the beginning of the bubble motion. Once the simulation commences, for a given value of S, the time step is adapted according to the following law: where H min is the minimum mean radius of curvature on the bubble's surface and ␣ an adjustable parameter that is initially set to one.…”

Section: Numerical Solutionmentioning

confidence: 99%

“…[14][15][16] For a review article on the boundary integral method for potential flow problems and comparative studies on the efficiency of different boundary integral formulations the interested reader is referred elsewhere. [17][18][19] Despite the fact that reliable solvers of the full NavierStokes equations have also been developed the boundary integral method is still widely applied due to its superiority in capturing details of severely deformed interfaces, with large accuracy and minimum computational effort. The weak viscous correction of the boundary integral method, such as the one employed here, extends the validity of the standard potential theory formulation, to the extent that large displacement thickness effects are not present.…”

Section: Numerical Solutionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear oscillations and collapse of elongated bubbles subject to weak viscous effects

Tsiglifis

Pelekasis

2005

Physics of Fluids

View full text Add to dashboard Cite

The weak viscous oscillations of a bubble are examined, in response to an elongation that perturbs the initial spherical shape at equilibrium. The flow field in the surrounding liquid is split in a rotational and an irrotational part. The latter satisfies the Laplacian and can be obtained via an integral equation. A hybrid boundary-finite element method is used in order to solve for the velocity potential and shape deformation of axisymmetric bubbles. Weak viscous effects are included in the computations by retaining first-order viscous terms in the normal stress boundary condition and satisfying the tangential stress balance. An extensive set of simulations was carried out until the bubble either returned to its initial spherical shape, or broke up. For a relatively small initial elongation the bubble returned to its initial spherical state regardless of the size of the Ohnesorge number; Oh= / ͑R͒ 1/2 . For larger initial elongations there is a threshold value in Oh −1 above which the bubble eventually breaks up giving rise to a "donut" shaped larger bubble and a tiny satellite bubble occupying the region near the center of the original bubble. The latter is formed as the round ends of the liquid jets that approach each other from opposite sides along the axis of symmetry, coalesce. The size of the satellite bubble decreased as the initial elongation or Oh −1 increased. This pattern persisted for a range of large initial deformations with a decreasing threshold value of the Oh −1 as the initial deformation increased. As its equilibrium radius increases the bubble becomes more susceptible to the above collapse mode. The effect of initial bubble overpressure was also examined and it was seen that small initial overpressures, for the range of initial bubble deformations that was investigated, translate the threshold of Oh −1 to larger values while at the same time increasing the size of the satellite bubble.

show abstract

Section: Numerical Solutionmentioning

confidence: 98%

Section: Numerical Solutionmentioning

confidence: 99%

Section: Numerical Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear oscillations and collapse of elongated bubbles subject to weak viscous effects

Tsiglifis

Pelekasis

2005

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…This step removes shortwavelength components and results in some numerical energy dissipation (Schulkes, 1994a). Other possibilities are the inclusion of numerical diffusion (Og uz and Prosperetti, 1990;Pelekasis, Tsamopoulos, and Manolis, 1992), or simply filtering of the short-wavelength components (Dold, 1992).…”

Section: A Inviscid Irrotational Flowmentioning

confidence: 99%

“…(12)-(15) in discrete numerical form, a number of different procedures were adopted, some of which are compared by Pelekasis, Tsamopoulos, and Manolis (1992). Usually the position of the interface x and the potential is taken at a discrete set of nodes i, 1рiрN.…”

Section: A Inviscid Irrotational Flowmentioning

confidence: 99%

Nonlinear dynamics and breakup of free-surface flows

1997

View full text Add to dashboard Cite

Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of the 19th century. Linear stability theory governs the onset of breakup and was developed by Rayleigh, Plateau, and Maxwell. However, only recently has attention turned to the nonlinear behavior in the vicinity of the singular point where a drop separates. The increased attention is due to a number of recent and increasingly refined experiments, as well as to a host of technological applications, ranging from printing to mixing and fiber spinning. The description of drop separation becomes possible because jet motion turns out to be effectively governed by one-dimensional equations, which still contain most of the richness of the original dynamics. In addition, an attraction for physicists lies in the fact that the separation singularity is governed by universal scaling laws, which constitute an asymptotic solution of the Navier-Stokes equation before and after breakup. The Navier-Stokes equation is thus continued uniquely through the singularity. At high viscosities, a series of noise-driven instabilities has been observed, which are a nested superposition of singularities of the same universal form. At low viscosities, there is rich scaling behavior in addition to aesthetically pleasing breakup patterns driven by capillary waves. The author reviews the theoretical development of this field alongside recent experimental work, and outlines unsolved problems. [S0034-6861(97)00303-6] CONTENTS

show abstract

Numerical simulation of coalescence of inviscid drops at a solid surface

Murray

1996

Commun. Numer. Meth. Engng.

View full text Add to dashboard Cite

SUMMARYA numerical method is used to simulate the motion of inviscid drops colliding and coalescing at a solid surface. The equations of motion are solved by a boundary element method in which the free surface of the drop is represented by a moving grid. The numerical results include the configuration of the drop during coalescence and the kinetic and potential energies. A numerical example is used to demonstrate the way in which coalescence affects the configuration of the free surface.

show abstract

A hybrid finite-boundary element method for inviscid flows with free surface

Cited by 26 publications

References 23 publications

Nonlinear oscillations and collapse of elongated bubbles subject to weak viscous effects

Nonlinear oscillations and collapse of elongated bubbles subject to weak viscous effects

Nonlinear dynamics and breakup of free-surface flows

Numerical simulation of coalescence of inviscid drops at a solid surface

Contact Info

Product

Resources

About