Time marching integral equation method for unsteady transonic flows around airfoils

A time marching integral equation method has been proposed here which does not have the limitation of the time linearized integral equation method in that the latter method can not satisfactorily simulate the shock wave motions. Firstly, a model problem–one dimensional initial and boundary value wave problem is treated to clarify the basic idea of the new method. Then the method is implemented for two dimensional unsteady transonic flow problems. The introduction of the concept of a quasi-velocity-potential simplifies the time marching integral equations and the treatment of trailing vortex sheet condition. The numerical calculations show that the method is reasonable and reliable.