Abstract: A new mathematical model for calculating the temperature field of the profile part of the cooled blades of gas turbines is developed. The theoretical substantiation of the method is based on the application of the method of potential theory (the method of boundary integral equations). The effectiveness of the implementation of the developed mathematical model is confirmed on the basis of a computational experiment.
Abstract: By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.
Abstract: Dynamics of a vapour bubble generated due to a high local energy input near a circular thin bronze plate in the absence of the buoyancy forces is numerically investigated in this paper. The bubble is generated near a thin bronze plate and during the growth and collapse of the bubble, it deforms the nearby plate. The Boundary Integral Equation Method is employed for numerical simulation of the problem. The fluid is assumed to be incompressible, irrotational and inviscid and the surface tension on the bubble boundary is neglected. Therefore the fluid flow around the vapour bubble can be assumed as a potential flow. Furthermore, the thin bronze plate is assumed to have perfectly plastic behaviour. Results show that the displacement of the circular thin bronze plate has considerable effect on the dynamics of its nearby vapour bubble. It is found that by decreasing the thickness of the thin bronze plate, the growth and collapse rate of the bubble becomes higher and consequently the lifetime of the bubble becomes shorter.
Abstract: Elastic boundary eigensolution problems are converted
into boundary integral equations by potential theory. The kernels of
the boundary integral equations have both the logarithmic and Hilbert
singularity simultaneously. We present the mechanical quadrature
methods for solving eigensolutions of the boundary integral equations
by dealing with two kinds of singularities at the same time. The methods
possess high accuracy O(h3) and low computing complexity. The
convergence and stability are proved based on Anselone-s collective
compact theory. Bases on the asymptotic error expansion with odd
powers, we can greatly improve the accuracy of the approximation,
and also derive a posteriori error estimate which can be used for
constructing self-adaptive algorithms. The efficiency of the algorithms
are illustrated by numerical examples.
Abstract: In this paper dynamics of a vapour bubble generated
due to a local energy input inside a vertical rigid cylinder and in the
absence of buoyancy forces is investigated. Different ratios of the
diameter of the rigid cylinder to the maximum radius of the bubble
are considered. The Boundary Integral Equation Method is employed
for numerical simulation of the problem. Results show that during
the collapse phase of the bubble inside a vertical rigid cylinder, two
liquid micro jets are developed on the top and bottom sides of the
vapour bubble and are directed inward. Results also show that
existence of a deposit rib inside the vertical rigid cylinder slightly
increases the life time of the bubble. It is found that by increasing the
ratio of the cylinder diameter to the maximum radius of the bubble,
the rate of the growth and collapse phases of the bubble increases
and the life time of the bubble decreases.
Abstract: In this paper, growth and collapse of a vapour bubble
generated due to a local energy input inside a rigid cylinder and in
the absence of buoyancy forces is investigated using Boundary
Integral Equation Method and Finite Difference Method .The fluid is
treated as potential flow and Boundary Integral Equation Method is
used to solve Laplace-s equation for velocity potential. Different
ratios of the diameter of the rigid cylinder to the maximum radius of
the bubble are considered. Results show that during the collapse
phase of the bubble inside a vertical rigid cylinder, two liquid micro
jets are developed on the top and bottom sides of the vapour bubble
and are directed inward. It is found that by increasing the ratio of the
cylinder diameter to the maximum radius of the bubble, the rate of
the growth and collapse phases of the bubble increases and the life
time of the bubble decreases.
Abstract: The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.
Abstract: In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.