Newton-Krylov continuation of periodic orbits for Navier-Stokes flows

Authors:
J. Sánchez;M. Net;B. García-Archilla;C. Simó
Affiliations:
Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado 1-3, Campus Nord UPC, Mòdul B4-B5, 08034 Barcelona, Spain;Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado 1-3, Campus Nord UPC, Mòdul B4-B5, 08034 Barcelona, Spain;Departamento de Matemática Aplicada II, Universidad de Sevilla, Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n, 41092 Sevilla, Spain;Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08071 Barcelona, Spain
Venue:
Journal of Computational Physics
Year:
2004

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Abstract

Efficient numerical algorithms for the continuation of periodic orbits of high-dimensional dissipative dynamical systems, and for analyzing their stability are presented. They are based on shooting, Newton-Krylov and Arnoldi methods. A thermal convection fluid dynamics problem, which has a rich bifurcation diagram due to symmetries, has been used as test. After a pseudo-spectral discretization of the equations a system of dimension O(104) has been obtained. The efficiency of the algorithms, which allows the unfolding of a complex diagram of periodic orbits, makes the methods suitable for the study of large nonlinear dissipative partial differential equations.