In this paper the boundary integral equation method has been employed for numerical simulation of the growth and collapse of a vapor bubble in a narrow cylindrical passage due to the emission of the ultrasound waves.
A boundary integral equation method based on the Green's integral formula and potential fluid flow theory has been employed for the numerical simulation of this problem.
They cover determining the velocity field by conformal mapping methods, calculating flat potential flows by the boundary integral equation method
, calculating vortex flows, the behavior of dust particles in the suction range, specific features of air ejected in a perforated duct with a bypass chamber, air ejection in a porous pipe with linear cross-flow pattern, specific features of air ejection in the elevator handling of grain, and measures for reducing aspiration volumes in the elevator handling of grain.
Now Let But for exterior flow problem the equation of indirect panel method for the doublet distribution can be stated as For exterior flow problem, assembling the equation (10) and equation (12) for the indirect boundary integral equation method
can be inscribed as Or When all nodes are in consideration, then equation (14) yields an system of equations which can be written in matrix form in the case of constant and linear elements as Here is the matrix coefficient, is a vector of unknown total potentials "and on the R.
The experimental results are compared with the results predicted by a numerical approach based on the boundary integral equation method
(BIEM) and the PHI3D package.
finite difference finite element and boundary integral equation methods
have limitations when the solution has the singularity on the boundary which is due to either a reentrant corner or to an abrupt change of boundary condition.