A new approach to the solution of large, full matrix equations: A twodimensional potential flow feasibility study
Abstract
An approach to the solution of matrix problems resulting from integral equations of mathematical physics is presented. Based on the inherent smoothness in such equations, the problem is reformulated using a set of orthogonal basis vectors, leading to an equivalent coefficient problem which can be of lower order without significantly impairing the accuracy of the solution. This approach was evaluated using a twodimensional Neumann problem describing the inviscid, incompressible flow over an airfoil. Two different kinds of mode functions were investigated, namely eigenfunction series and Fourier series. The method using Fourier series was found preferable. It uses all of the coefficients from a Fast Fourier Transform algorithm in an approximate method which exploits the known structure of the transformed coefficient matrix and very promising results for the flow over a realistic airfoil are obtained. On the basis of the results presented here, an order of magnitude reduction in this computer time can be expected for such problems as compared with the time for a direct matrix solution.
 Publication:

Final Report Douglas Aircraft Co
 Pub Date:
 September 1979
 Bibcode:
 1979daci.rept.....J
 Keywords:

 Eigenvectors;
 Fast Fourier Transformations;
 Feasibility Analysis;
 Two Dimensional Flow;
 Airfoils;
 Algorithms;
 Computer Programs;
 Integral Equations;
 Inviscid Flow;
 Fluid Mechanics and Heat Transfer