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This study presents a new approach to calculate the velocities (normal and tangential components) in a potential flow adopting the Boundary Element Method BEM, with hypersingular formulation. The hypersingular equation is established based on the directional derivative of the potential at an internal point of the domain. When this expression is applied to the boundary points, through a limits process, singularities appear. Vectorial algebra is used in order to write the free terms of the integral equation independent of the co-ordinates system, rendering their calculation mainly geometrical. The final expressions, in integral formulations and continuity conditions, are presented to calculate the normal and tangential velocity field of the boundary. The theory developed is computationally implemented for constant, linear and quadratic elements. Several simulation results to validate the technique are presented, in which the effect of discretizations can be observed when the conditions for their existence are not fulfilled or, conversely, when they are correctly fulfilled.

Obtenção do Campo de Velocidades em Escoamentos Potenciais por uma Formulação Hiper-Singular do Método dos Elementos de Contorno.