The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution.This algorithm is matrix-free and emp...The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution.This algorithm is matrix-free and employs a combination of the Newton-Raphson method and the Krylov subspace method.Moreover,the algorithm adopts a multiple shooting method to address the problem of orbital instability due to long-term numerical integration.The algorithm is described through computing the extension of unstable manifold of a recomputed Nagata′s lowerbranch steady solution of plane Couette flow,which is an example of an exact coherent state that has recently been studied in subcritical transition to turbulence.展开更多
文摘The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution.This algorithm is matrix-free and employs a combination of the Newton-Raphson method and the Krylov subspace method.Moreover,the algorithm adopts a multiple shooting method to address the problem of orbital instability due to long-term numerical integration.The algorithm is described through computing the extension of unstable manifold of a recomputed Nagata′s lowerbranch steady solution of plane Couette flow,which is an example of an exact coherent state that has recently been studied in subcritical transition to turbulence.
