Finding leading modes of a viscous free surface flow: An asymmetric generalized eigenproblem. (English) Zbl 0677.65032

The paper presents a computational procedure for investigating the stability of steady, two-dimensional, slide coating flow of Newtonian liquid to small, two-dimensional disturbances. The analysis is done by means of Galerkin’s method and finite element basis functions. The resulting computational task consists for large \((n>2000)\) sparse, nonsymmetric and banded singular generalized eigenproblems in which the matrices depend on system parameters. These eigenproblems are solved for a few leading modes (eigenvalues of largest real part and the corresponding eigenvectors) by a flexible method assembled from the iterative Arnoldi algorithm with Schur-Wielandt deflation; initialization that can incorporate rational acceleration; real or complex shift of eigenvalues and approximately exponential preconditioning by rational transformation.
Reviewer: Petko Hr.Petkov


65F15 Numerical computation of eigenvalues and eigenvectors of matrices
76D05 Navier-Stokes equations for incompressible viscous fluids


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