A High Order Compact Scheme for the Pure-Streamfunction Formulation of the Navier-Stokes Equations

@article{BenArtzi2010AHO,
  title={A High Order Compact Scheme for the Pure-Streamfunction Formulation of the Navier-Stokes Equations},
  author={Matania Ben-Artzi and Jean-Pierre Croisille and Dalia Fishelov},
  journal={J. Sci. Comput.},
  year={2010},
  volume={42},
  pages={216-250}
}
In this paper we continue the study, which was initiated in [10, 28, 9, 7], of the numerical resolution of the pure streamfunction formulation of the timedependent two-dimensional Navier-Stokes equation. Here we focus on enhancing our second-order scheme, introduced in [28, 9, 7], to fourth order accuracy. We construct fourth order approximations for the Laplacian, the biharmonic and the nonlinear convective operators. The scheme is compact (nine-point stencil) for the Laplacian and the… CONTINUE READING
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