Boundary Element Solution of the Transonic Integro-Differential Equation Involving a Decay Function

摘要

The transonic integro-differential equation is solved using a decay function which can be applied in front and aft of the airfoil rather than on the airfoil surface only. The computational domain is discretized into rectangular elements and the integrals involving the dependent variable are approximated by boundary element methods in each rectangle. Besides constant elements, use is made of hybrid elements which are based on constant elements in the streamwise direction and variable elements in the transverse direction. The matrix elements are computed once and stored but the described method leads to considerable savings in storage space. The methods are tested for parabolic-arc and NACA0012 airfoils in subcritical and supercritical flows and the results compare well with finite difference solutions. It is concluded that hybrid elements provide good accuracy even with only one horizontal strip of rectangular elements, which implies a relatively small number of nodes. (author). 18 refs, 6 figs, 3 tabs. (Atomindex citation 19:047404)