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The complex variable boundary element method (CVBEM) owes its elegance, the computational accuracy and efficiency, to the Cauchy's integral formula, and it can be interpreted as a semi-analytical scheme. Despite its sound mathematical foundations, the real performance of the CVBEM may be affected by its computational foundations. This study focuses on two of such fundamental aspects: the formulations of the CVBEM and the treatment of sink and source singularities. Here proposed are three types of formulations for the CVBEM, and their performances are assessed. Formulation I using known-variable equivalence may accumulate errors on unprescribed boundaries resulting in severe oscillation in error profiles. Formulation II using unknown-variable equivalence yields error profiles that are smoother and smaller than those of Formulation I. Formulation III using dual-variable equivalence yields the best accuracy among the three. By virtue of the semi-analytic nature of the CVBEM, the singularity programming, which separates singular and non-singular solutions, can be applied to the CVBEM. Non-singular flow behaves smoothly, and the CVBEM yields accurate non-singular solutions. A complete solution is obtained by adding an analytic singular solution to the non-singular solution. With the singularity programming, the CVBEM can handle the sink and source singularities without a loss of accuracy.

Formulations of the Complex Variable Boundary Element Method for Potential Flow with Sink and Source Singularities.