| In this paper,the boundary integral equation of Stokes problem is solved by fast Fourier-Galerkin method.In this method,the coefficient matrix of the discrete system is a numerical sparse matrix whose most elements are approx-imately zero.This is a better convergence method,which is characterized by high precision and less time.In plane Stokes equation,the original problem is transformed into the boundary integral equation by the single-layer potential theory.The inte-gral boundary is a smooth closed curve.After coordinate transformation,it is transformed into one-dimensional boundary integral equation with only one variable.Then we decompose the singular integral kernel function of the boundary integral equation into a singular function and a smooth function which grasp the main singular part.The singular part is transformed into a diagonal matrix by using the properties of the orthogonal basis and the char-acteristic function.The smooth part is directly calculated by using the fast Fourier transform.The three-dimensional axisymmetric Stokes internal problem is solved by the potential theory of fluid mechanics.The integral surface is a three-dimensional rotationally symmetric surface,so the dimension of the problem is reduced by using coordinate transformation.The integral kernel of the transformed boundary integral equation is singular.Then we deal with the singular kernel function.In the same way,we choose the orthogonal basis as the basis function to transform the singular part into the diagonal matrix,and the smooth part still uses the fast Fourier transform for numerical calculation. |
