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An Alternative Approach in the Study of Potential Wind Flow by the Boundary Element Method

The method for a study of the two-dimensional (plane) potential wind-flow is presented. The wind velocity is gradient of so-called velocity potential that satisfies Laplace's differential equation. Partial integration leads to integral equation that has to be solved in the respect to the specific boundary conditions. The problem arises from the fact that solid is in the wind stream that is definable as undisturbed only enough far from the solid. Therefore, it is convenient to develop analytical solution of those integrals by which the boundary conditions that corresponds to undisturbed wind-flow are integrated. The integral equation is approximated with the system of linear equations by the application of the so-called boundary element method. The unknowns in those equations are usually the velocity potentials at the chosen set of the boundary points, while wind velocities at the any point in the space need to be calculated as gradient of velocity potential. In the purpose to provide advance, the solid surface can be substituted with linear distribution of wind sources (or sinks). That result with simplified integral equation and joined system of linear equations, in which the unknowns are intensities of wind sources. In that case, the wind velocity at the any point in the space can be calculated by simple integration of intensity distribution of those wind sources. Since in the proposed equations some integrals over boundary partially vanish, number of numerical operations is reduced, while a computer program becomes shorter.

potential wind flow; boundary element method; integral equation

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