A SEMI-ANALYTICAL METHOD FOR A FLOW OF NON-VISCOUS FLUID AROUND AN AIRFOIL WITH A SHARP TRAILING EDGE

In the present work we propose a method to study a two-dimensional flow of non-viscous fluid around an airfoil with a sharp trailing edge, by the double-layer potential theory. The circulation of velocity vector is modeled by the potential of a point vortex whose center is located inside the boundary contour. The magnitude of the circulation is defined on the basis of the Joukowski-Chaplygin postulate. There are presented some results for a Joukowski rudde, as well as for the airfoil in the form of a pair of interacting circles. It is performed a comparison of the circulation with its theoretical value.

Light Curve Calculations for Triple Microlensing Systems

We present a method to compute the magnification of a finite source star lensed by a triple lens system based on the image boundary (contour integration) method. We describe a new procedure to obtain continuous image boundaries from solutions of the tenth-order polynomial obtained from the lens equation. Contour integration is then applied to calculate the image areas within the image boundaries, which yields the magnification of a source with uniform brightness. We extend the magnification calculation to limb-darkened stars approximated with a linear profile. In principle, this method works for all multiple lens systems, not just triple lenses. We also include an adaptive sampling and interpolation method for calculating densely covered light curves. The C++ source code and a corresponding Python interface are publicly available.

Algorithm for using the boundary element method on the example of a mixed boundary value problem for the Poisson equation

The possibilities of the algorithm for applying the boundary element method to solving boundary value problems are discussed on the example of the two-dimensional Poisson differential equation. The algorithm does not change significantly when the type of boundary conditions changes: the Dirichlet problem, the Neumann problem, or a mixed boundary value problem. The idea of the algorithm is taken from the work of John T. Katsikadelis [1]. The algorithm is described in detail in the next sequence of actions. 1) The boundary- value problem for a two-dimensional finite domain is formulated. The desired function in the domain, its values, and its normal derivative on the boundary contour are connected by means of the second Green formula. 2) We pass from the boundary value problem for the Poisson equation to the boundary value problem for the Laplace equation. This simplifies the process of constructing an integral equation. We obtain the integral equation on the boundary contour using the boundary conditions. 3) In the integral equation, we divide the boundary contour into a finite number of boundary elements. The desired function and its normal derivative are considered constant values on each boundary element. We compose a system of linear algebraic equations considering these values. 4) We modify the system of linear algebraic equations taking into account the boundary conditions. After that, we solve it using the Gauss method. The computer program has been developed according to the developed algorithm. We used it in the learning process. The software implementation of the algorithm takes into account the capabilities of modern computer technology and modern needs of the educational process. The work of the program is shown in the test case. Further modification of the described algorithm is possible