Boundary spectral methods for non-lifting potential flows

The boundary spectral method for solving three-dimensional non-lifting potential problems is developed. This method combines spectral approximations and the direct numerical integration such as Gaussian quadrature or trapezoidal rules successfully. The singularities of the integral equation are completely removed by subtracting known solutions from the Laplace equation. After discretization, every element of the resultant matrix only contains integrals with non-singular kernels. Therefore, all the integrals can be implemented easily and e¦ciently. By spectral approximations, the unknown variable is expressed as a truncated series of basis functions, which are orthogonal usually. Instead of solving the variables at collocation points in the conventional methods, the coe¦cients of basis functions are determined in the spectral approach. It is shown that the new method reduces a lot of number of unknowns, storage of matrix elements, and computer time for solving the algebraic equations