High-Order Schemes in Boundary Element Methods for Transient Non-Linear Free Surface Problems

Machane, Rabha; Canot, Édouard

doi:10.1002/(sici)1097-0363(19970530)24:10<1049::aid-fld531>3.0.co;2-4

Cited by 13 publications

(11 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Following an explicit numerical scheme [19] improved for the capillary [20], and viscous effects [15,21], the time progression is made through second-order limited Taylor series expansions:…”

Section: Methodsmentioning

confidence: 99%

Jet drops ejection in bursting gas bubble processes

Georgescu

Achard

Canot

2002

European Journal of Mechanics - B/Fluids

View full text Add to dashboard Cite

The numerical simulation using a boundary element method is presented for a gas bubble bursting at a free surface in a potential flow with a viscous fluid assumption. Systematic comparisons are given with experimental data on the first "jet drop" size in relation with the parent bubble size, and on the critical bubble radius above which no jet drop forms. The computations were made for different liquids. It is pointed out that an exact description of the jet formation and break up requires the complete Navier-Stokes equations only in the final phase of the evolution.

show abstract

Section: Methodsmentioning

confidence: 99%

Jet drops ejection in bursting gas bubble processes

Georgescu

Achard

Canot

2002

European Journal of Mechanics - B/Fluids

View full text Add to dashboard Cite

show abstract

“…As a result, for every time step ∆t we have to solve several Laplace problems in different geometries. More precisely, four computations of the integral equations are required at each iteration and that can be time-consuming in comparison with an explicit high-order Taylor series expansion 1 (Machane and Canot, 1997). Here, the Runge-Kutta method suits our problem particularly well since, during the draining stage, the typical mesh size becomes smaller and smaller.…”

Section: Time-stepping Methodsmentioning

confidence: 99%

“…Useful material for this classical direct approach can be found in Brebbia et al (1984). In our particular case, however, the boundary geometry is approximated by cubic splines and use is made of a cubic Hermite polynomial approximation for the field functions (Machane and Canot, 1997): this choice has been proved to provide good accuracy in interface-tracking problems.…”

Section: Spatial Discretisation For the Bemmentioning

confidence: 99%

Numerical Simulation of the Buoyancy-Driven Bouncing of a 2-D Bubble at a Horizontal Wall

Canot

Davoust

Hammoumi

et al. 2003

Theoretical and Computational Fluid Dynamics

View full text Add to dashboard Cite

Abstract. The rise of a buoyant bubble and its interaction with a target horizontal wall is simulated with a 2-D numerical code based on the Boundary Element Method (BEM). Developed from a viscous potential flow approximation, the BEM takes into account only the part of the energy dissipation related to the normal viscous stresses. Hence, a simple analytical model based on lubrication approximation is coupled to the BEM in order to compute the drainage of the interstitial liquid film filling the gap between the bubble and the near wall. In this way the bubble-wall interaction is fully computed: the approach stage, the bubble deformation stage and, depending on the values of the Reynolds number and the Weber number, the rebound and the bubble oscillations. From computation of both the bubble interface motion and the liquid velocity field, a physical analysis in terms of energy budget is proposed. Though, in the present study, the bubble under consideration is basically supposed to be a 2-D gaseous cylinder, a comparison between our numerical results and the experiments of Tsao and Koch (1997) enlightens interestingly the physics of bouncing.

show abstract

“…The TSE was successfully used to simulate two-dimensional sloshing problems by Liu et al [11]. Machane and Canot [12] further concluded that the TSE is more efficient than the Runge-Kutta method in the time marching for the CPU time. Since then, many literatures have used similar ideas to demonstrate that their schemes are successful for two-dimensional computation.…”

Section: Introductionmentioning

confidence: 99%

Sloshing behaviours of rectangular and cylindrical liquid tanks subjected to harmonic and seismic excitations

Chen

Hwang

2007

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

A numerical and experimental study on the sloshing behaviours of cylindrical and rectangular liquid tanks is addressed. A three-dimensional boundary element method for space with the second-order Taylor series expansion in time is established to simulate the sloshing phenomenon and its related physical quantities inside a liquid tank subjected to horizontal harmonic oscillations or recorded earthquake excitations. The small-scale model experiments are carried out to verify some results of numerical methods in this study. The comparisons between numerical and experimental results show that the numerical method is reliable for both kinds of ground excitations. Finally, the water wave and the base shear force of a rectangular tank due to harmonic excitation are also presented at different frequencies. A huge cylindrical water tank subjected to a recorded earthquake excitation is used for application and discussion.

show abstract

High-Order Schemes in Boundary Element Methods for Transient Non-Linear Free Surface Problems

Cited by 13 publications

References 13 publications

Jet drops ejection in bursting gas bubble processes

Jet drops ejection in bursting gas bubble processes

Numerical Simulation of the Buoyancy-Driven Bouncing of a 2-D Bubble at a Horizontal Wall

Sloshing behaviours of rectangular and cylindrical liquid tanks subjected to harmonic and seismic excitations

Contact Info

Product

Resources

About