Accurate calculation of weak singular integrals in boundary element method in moving flows

A key issue of the boundary element method(BEM) was usually used to study the acoustic radiation in moving medium is how to calculate the weak integrals when the field point approaches to the source point.A new integral method was developed to solve this problem,in which the weak integral on the element surface was divided into singular integral and non-singular integral.For the singular part,analytic solution was obtained through rigorous mathematic derivation.As to the non-singular part,the integral was evaluated by numerical quadrature technique.One of the major advantages of the method is the good accuracy to was that it could effectively compute the singular integrals.