Steady two-dimensional transonic analysis using a boundary integral equation method

A boundary integral equation method for the simulation of two-dimensional steady transonic potential flows is presented. The method is based on a conservative differential full-potential formulation. The steady two-dimensional formulation is obtained as the limiting case of the unsteady three-dimensional one, as the iterative method used to obtain steady-state results is a pseudo-time-accurate three-dimensional technique. In the present formulation the full-potential equation appears in the form of a nonlinear wave equation for the velocity potential. All the nonlinear terms, which are expressed in conservative form, are moved to the right-hand side, and treated formally as nonhomogeneous terms. The paper includes a historical review on the development of integral formulations for transonic analysis. Numerical results are obtained for steady two-dimensional transonic flaws. Comparisons with existing finite-difference, finite-element, and finite-volume results shows a good agreement. The convergence analysis for an increasing number of grid elements reveals a limit behaviour in good agreement with other numerical methods in both subcritical and supercritical problems. Finally, we present numerical results to demonstrate a remarkable feature of the formulation, that is that the transonic numerical results are quite insensitive to the geometry of the field volume elements; this makes the present formulation particularly appealing for optimal design applications. (C) 1997 Academic Press Limited.