SPATIAL INSTABILITIES OF THE INCOMPRESSIBLE ATTACHMENT-LINE FLOW USING SPARSE-MATRIX JACOBI-DAVIDSON TECHNIQUES

We consider the linear stability of incompressible attachment-line flo w within the spatial framework. No similarity or symmetry assumptions for the instability modes are introduced and the full two-dimensional representation of the modes is used. The perturbation equations are di scretized on a two-dimensional staggered grid. A high order finite dif ference scheme has been developed which gives rise to a large, sparse, quadratic, eigenvalue problem for the instability modes. The benefits of the Jacobi-Davidson method for the solution of this eigenvalue sys tem are demonstrated and the approach is validated in some detail. Spa tial stability results are presented subsequently. In particular, inst ability predictions at very high Reynolds :numbers are obtained which show almost equally strong instabilities for symmetric and antisymmetr ic modes in this regime.