BOUNDARY SPECTRAL METHODS FOR NONLIFTING POTENTIAL FLOWS

The boundary spectral method for solving three-dimensional non-lifting potential problems is developed. This method combines spectral approx imations and the direct numerical integration such as Gaussian quadrat ure or trapezoidal rules successfully. The singularities of the integr al equation are completely removed by subtracting known solutions from the Laplace equation. After discretization, every element of the resu ltant matrix only contains integrals with non-singular kernels. Theref ore, all the integrals can be implemented easily and efficiently. By s pectral approximations, the unknown variable is expressed as a truncat ed series of basis functions, which are orthogonal usually. Instead of solving the variables at collocation points in the conventional metho ds, the coefficients 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 th e algebraic equations. (C) 1998 John Wiley & Sons, Ltd.