A u,v-formulation for ideal fluid flow

By using the velocity components as basic unknowns, Doctors (1970) has studied two-dimensional incompressible irrotational inviscid fluid flow for the ideal case. Doctors' approach may be interpreted as an application of the subdomain collocation in the method of weighted residuals. In this paper, the least square method is adopted to achieve a symmetric coefficient matrix. The velocity components are of more direct physical interest than the velocity potential or the stream function usually employed in solving problems of this nature. A simplified method for treating the lifting surface case is also discussed.