BOUNDARY INTEGRAL FORMULATION FOR THE COLLAPSE OF AN INITIALLY SPHERICAL VAPOR CAVITY UNDER THE EFFECT OF THE CURVATURE

1995 ◽  
Vol 05 (07) ◽  
pp. 923-933
Author(s):  
A. PIACENTINI
Keyword(s):  
Surface Tension ◽  
Boundary Element Method ◽  
Mathematical Models ◽  
Spline Approximation ◽  
Boundary Integral ◽  
Small Radius ◽  
Bubble Collapse ◽  
Linear Boundary ◽  
Vapor Cavity ◽  
Boundary Integral Formulation

The effect of the curvature is usually neglected in the mathematical models of bubble collapse. For bubbles of sufficiently small radius such effect becomes of relevant interest. A linear boundary element method (B.E.M.) with a cubic spline approximation of the domain that takes the surface tension into account is presented.

A Boundary Element Method for Multi-Body Contact Problems and its Application to the Analysis of a Huge Excavator

1995 ◽  
Author(s):  
Chong-De Liu ◽  
Jiyuan Yu ◽  
Xiaoming Wang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Contact Problems ◽  
Fortran Program ◽  
Boundary Integral ◽  
Element Formulation ◽  
Body Contact ◽  
Boundary Integral Formulation ◽  
Discretization Technique ◽  
Multi Body

Abstract The derivation of a boundary integral formulation and discretization technique in terms of boundary elements for the solution of multi-body contact problems has been carried out. A FORTRAN program has been developed based on this boundary element formulation and has been applied to the stress analysis of a huge caterpillar excavator woth 16 m3 bucket capacity.

On the impulsive generation of drops at the interface of two inviscid fluids

2008 ◽  
Vol 464 (2093) ◽  
pp. 1125-1140 ◽  
Author(s):  
K.K Tjan ◽  
W.R.C Phillips
Keyword(s):  
Phase Diagram ◽  
Surface Tension ◽  
Density Ratio ◽  
Boundary Integral ◽  
Inviscid Fluid ◽  
Fluid Interface ◽  
Inviscid Fluids ◽  
Boundary Integral Formulation ◽  
Lower Fluid ◽  
Density Ratios

The numerical simulation of the deformation of an inviscid fluid–fluid interface subjected to an axisymmetric impulse in pressure is considered. Using a boundary integral formulation, the interface is evolved for a range of upper-fluid and lower-fluid density ratios under the influence of inertial, interfacial and gravitational forces. The interface is seen to evolve into axisymmetric waves or droplets depending upon the density ratio, level of surface tension and gravity. Moreover, the droplets may be spherical, tear shaped or elongated. These conclusions are expressed in a phase diagram of inverse Weber number We −1 versus Atwood number At at zero gravity, i.e. with the Froude number Fr −1 →0, and complement the earlier findings of Tjan & Phillips, who present a phase diagram of We −1 versus Fr −1 for the case in which the upper fluid has zero density. They too report tear-shaped droplets; however, while, in their paper, they form as a result of gravity, those reported here form as a result of surface tension. It is also found that the pinch-off process which effects drops remains of the power-law type with exponent 2/3 irrespective of the presence of gravity and an upper fluid. However, the constant that relates the necking radius to the time from pinch off, which is universal in the absence of gravity and an upper fluid, is affected by the presence gravity, an upper fluid and the class of drops which form.

scholarly journals Vortex ring bubbles

1991 ◽  
Vol 224 ◽  
pp. 177-196 ◽  
Author(s):  
T. S. Lundgren ◽  
N. N. Mansour
Keyword(s):  
Surface Tension ◽  
Vortex Ring ◽  
Model Equation ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Liquid Jet ◽  
General Description ◽  
Boundary Integral Formulation ◽  
Ring Radius ◽  
Toroidal Geometry

Toroidal bubbles with circulation are studied numerically and by means of a physically motivated model equation. Two series of computations are performed by a boundary-integral method. One set shows the starting motion of an initially spherical bubble as a gravitationally driven liquid jet penetrates through the bubble from below causing a toroidal geometry to develop. The jet becomes broader as surface tension increases and fails to penetrate if surface tension is too large. The dimensionless circulation that develops is not very dependent on the surface tension. The second series of computations starts from a toroidal geometry, with circulation determined from the earlier series, and follows the motion of the rising and spreading vortex ring. Some modifications to the boundary-integral formulation were devised to handle the multiply connected geometry. The computations uncovered some unexpected rapid oscillations of the ring radius. These oscillations and the spreading of the ring are explained by the model equation which provides a more general description of vortex ring bubbles than previously available.

Numerical solution of the exact equations for capillary–gravity waves

1979 ◽  
Vol 95 (1) ◽  
pp. 119-139 ◽  
Author(s):  
Leonard W. Schwartz ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Numerical Solution ◽  
Gravity Waves ◽  
High Accuracy ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Boundary Equation ◽  
Boundary Integral Formulation ◽  
Wave Forms ◽  
Nonlinear Form

A numerical method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The dynamic boundary equation is used in its exact nonlinear form. The procedure involves a boundary-integral formulation coupled with a Newtonian iteration. Solutions of high accuracy can be achieved over much of the range of wavelengths and heights including limiting waves. A number of different continuous families of solutions have been produced, all of which ultimately exhibit closed bubbles at their troughs. The so-called critical wavelengths are less important than have been previously assumed; the number of possible wave forms does increase with increasing wavelength, however.

scholarly journals Geometric series expansion of the Neumann–Poincaré operator: Application to composite materials

2021 ◽  
pp. 1-26
Author(s):  
ELENA CHERKAEV ◽  
MINWOO KIM ◽  
MIKYOUNG LIM
Keyword(s):  
Composite Materials ◽  
Series Expansion ◽  
Function Theory ◽  
Effective Conductivity ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Geometric Function Theory ◽  
Boundary Integral Formulation ◽  
Geometric Function ◽  
Series Expression

The Neumann–Poincaré (NP) operator, a singular integral operator on the boundary of a domain, naturally appears when one solves a conductivity transmission problem via the boundary integral formulation. Recently, a series expression of the NP operator was developed in two dimensions based on geometric function theory [34]. In this paper, we investigate geometric properties of composite materials using this series expansion. In particular, we obtain explicit formulas for the polarisation tensor and the effective conductivity for an inclusion or a periodic array of inclusions of arbitrary shape with extremal conductivity, in terms of the associated exterior conformal mapping. Also, we observe by numerical computations that the spectrum of the NP operator has a monotonic behaviour with respect to the shape deformation of the inclusion. Additionally, we derive inequality relations of the coefficients of the Riemann mapping of an arbitrary Lipschitz domain using the properties of the polarisation tensor corresponding to the domain.

scholarly journals An Advance-Tracing Boundary Element Method in the Time Domain for Solving the Radiating Problem of an Arbitrary Obstacle Accelerating Randomly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jui-Hsiang Kao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Boundary Integral ◽  
Normal Velocity ◽  
Time Step ◽  
Random Acceleration ◽  
The Time Domain ◽  
First Time ◽  
Element Method

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

Sign in / Sign up

Export Citation Format

Share Document