Bifurcation analysis of two-dimensional Rayleigh-Bénard convection using deflation

  title={Bifurcation analysis of two-dimensional Rayleigh-B{\'e}nard convection using deflation},
  author={Nicolas Boull'e and Vassilios Dallas and Patrick E. Farrell},
  journal={Physical review. E},
  volume={105 5-2},
We perform a bifurcation analysis of the steady states of Rayleigh-Bénard convection with no-slip boundary conditions in two dimensions using a numerical method called deflated continuation. By combining this method with an initialization strategy based on the eigenmodes of the conducting state, we are able to discover multiple solutions to this nonlinear problem, including disconnected branches of the bifurcation diagram, without the need for any prior knowledge of the solutions. One of the… 

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