The Martin-Lomax Iteration for the Computations of Transonic Flow Fields - Some Observations.
Abstract
The iteration method of Martin and Lomax for the computation of transonic flow fields is applied to some linear examples (subsonic flows, supersonic flows, and flows with a shock). In these examples a Fourier decomposition can be made in one coordinate direction, and one is left with a one-dimensional difference equation. The question of compatibility of the boundary conditions pertaining to the elliptic operator used in the Martin-Lomax iteration, with those of a hyperbolic problem is discussed. The one-dimensional difference procedure gives rise to a linear eigenvalue problem. The distribution of the eigenvalues and the form of the eigenvectors explains the convergence behavior of solutions obtained with different initial which occur in the influence of certain arbitrary parameters which occur in the Martin-Lomax procedure is briefly discussed. An attempt is made to improve the convergence of the iterations by the application of Aitken-Shanks formulae of different orders. A direct derivation of the concept underlying these formulae is given. In the present examples, the Aitken-Shanks extrapolation failed to accelerate the convergence.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1979
- Accession Number
- ADA072523
Entities
People
- Donald S. Clemm
- Karl G. Guderley
Organizations
- University of Dayton